## Members

## Publications

### 2020

[Ablinger]

### Proving Two Conjectural Series for $\zeta(7)$ and Discovering More Series for $\zeta(7)$

#### J. Ablinger

In: Mathematical Aspects of Computer and Information Science, D. Slamanig, E. Tsigaridas, Z. Zafeirakopoulos (ed.), pp. 42-47. 2020. Springer International Publishing, 978-3-030-43120-4. [url]@

author = {J. Ablinger},

title = {{Proving Two Conjectural Series for $\zeta(7)$ and Discovering More Series for $\zeta(7)$}},

booktitle = {{Mathematical Aspects of Computer and Information Science}},

language = {english},

pages = {42--47},

publisher = {Springer International Publishing},

isbn_issn = {978-3-030-43120-4},

year = {2020},

editor = {D. Slamanig and E. Tsigaridas and Z. Zafeirakopoulos},

refereed = {yes},

length = {6},

url = {https://arxiv.org/abs/1908.06631v1}

}

**inproceedings**{RISC6102,author = {J. Ablinger},

title = {{Proving Two Conjectural Series for $\zeta(7)$ and Discovering More Series for $\zeta(7)$}},

booktitle = {{Mathematical Aspects of Computer and Information Science}},

language = {english},

pages = {42--47},

publisher = {Springer International Publishing},

isbn_issn = {978-3-030-43120-4},

year = {2020},

editor = {D. Slamanig and E. Tsigaridas and Z. Zafeirakopoulos},

refereed = {yes},

length = {6},

url = {https://arxiv.org/abs/1908.06631v1}

}

[Ablinger]

### Subleading logarithmic QED initial state corrections to $e^+e^−\to γ^⁎/Z^{0⁎}$ to $O(\alpha^6L^5)$

#### J. Ablinger, J. Blümlein, A. De Freitas, K. Schönwald

Nuclear Physics B 955, pp. 115045-115045. 2020. ISSN 0550-3213. [url]@

author = {J. Ablinger and J. Blümlein and A. De Freitas and K. Schönwald},

title = {{Subleading logarithmic QED initial state corrections to $e^+e^−\to γ^⁎/Z^{0⁎}$ to $O(\alpha^6L^5)$}},

language = {english},

journal = {Nuclear Physics B},

volume = {955},

pages = {115045--115045},

isbn_issn = { ISSN 0550-3213},

year = {2020},

refereed = {yes},

length = {0},

url = {http://www.sciencedirect.com/science/article/pii/S0550321320301310}

}

**article**{RISC6111,author = {J. Ablinger and J. Blümlein and A. De Freitas and K. Schönwald},

title = {{Subleading logarithmic QED initial state corrections to $e^+e^−\to γ^⁎/Z^{0⁎}$ to $O(\alpha^6L^5)$}},

language = {english},

journal = {Nuclear Physics B},

volume = {955},

pages = {115045--115045},

isbn_issn = { ISSN 0550-3213},

year = {2020},

refereed = {yes},

length = {0},

url = {http://www.sciencedirect.com/science/article/pii/S0550321320301310}

}

[Cerna]

### Unital Anti-Unification: Type and Algorithms

#### David M. Cerna , Temur Kutsia

Technical report no. 20-02 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. RISC Report, Febrary 2020. [pdf]@

author = {David M. Cerna and Temur Kutsia},

title = {{Unital Anti-Unification: Type and Algorithms}},

language = {english},

abstract = {Unital equational theories are defined by axioms that assert the existence of the unit element for some function symbols. We study anti-unification (AU) in unital theories and address the problems of establishing generalization type and designing anti-unification algorithms. First, we prove that when the term signature contains at least two unital functions, anti-unification is of the nullary type by showing that there exists an AU problem, which does not have a minimal complete set of generalizations. Next, we consider two special cases: the linear variant and the fragment with only one unital symbol, and design AU algorithms for them. The algorithms are terminating, sound, complete and return tree grammars from which set of generalizations can be constructed. Anti-unification for both special cases is finitary. Further, the algorithm for the one-unital fragment is extended to the unrestricted case. It terminates and returns a tree grammar which produces an infinite set of generalizations. At the end, we discuss how the nullary type of unital anti-unification might affect the anti-unification problem in some combined theories, and list some open questions. },

number = {20-02},

year = {2020},

month = {Febrary},

howpublished = {RISC Report},

keywords = {Anti-unification, tree grammars, unital theories, collapse theories},

length = {19},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

**techreport**{RISC6080,author = {David M. Cerna and Temur Kutsia},

title = {{Unital Anti-Unification: Type and Algorithms}},

language = {english},

abstract = {Unital equational theories are defined by axioms that assert the existence of the unit element for some function symbols. We study anti-unification (AU) in unital theories and address the problems of establishing generalization type and designing anti-unification algorithms. First, we prove that when the term signature contains at least two unital functions, anti-unification is of the nullary type by showing that there exists an AU problem, which does not have a minimal complete set of generalizations. Next, we consider two special cases: the linear variant and the fragment with only one unital symbol, and design AU algorithms for them. The algorithms are terminating, sound, complete and return tree grammars from which set of generalizations can be constructed. Anti-unification for both special cases is finitary. Further, the algorithm for the one-unital fragment is extended to the unrestricted case. It terminates and returns a tree grammar which produces an infinite set of generalizations. At the end, we discuss how the nullary type of unital anti-unification might affect the anti-unification problem in some combined theories, and list some open questions. },

number = {20-02},

year = {2020},

month = {Febrary},

howpublished = {RISC Report},

keywords = {Anti-unification, tree grammars, unital theories, collapse theories},

length = {19},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

[Cerna]

### Aiding an Introduction to Formal Reasoning Within a First-Year Logic Course for CS Majors Using a Mobile Self-Study App

#### David M. Cerna and Martina Seidl and Wolfgang Schreiner and Wolfgang Windsteiger and Armin Biere

In: ITICSE 2020, ACM (ed.), pp. 1-7. 2020. https://doi.org/10.1145/3341525.3387409.@

author = {David M. Cerna and Martina Seidl and Wolfgang Schreiner and Wolfgang Windsteiger and Armin Biere},

title = {{Aiding an Introduction to Formal Reasoning Within a First-Year Logic Course for CS Majors Using a Mobile Self-Study App}},

booktitle = {{ITICSE 2020}},

language = {english},

abstract = {In this paper, we share our experiences concerning the introduc-tion of the Android-based self-study app AXolotl within the first-semester logic course offered at our university. This course is manda-tory for students majoring in Computer Science and Artificial In-telligence. AXolotl was used as part of an optional lab assignmentbridging clausal reasoning and SAT solving with classical reason-ing, proof construction, and first-order logic. The app provides anintuitive interface for proof construction in various logical calculiand aids the students through rule application. The goal of thelab assignment was to help students make a smoother transitionfrom clausal and decompositional reasoning used earlier in thecourse to inferential and contextual reasoning required for proofconstruction and first-order logic. We observed that the lab had apositive influence on students’ understanding and end the paperwith a discussion of these results.},

pages = {1--7},

isbn_issn = {https://doi.org/10.1145/3341525.3387409},

year = {2020},

editor = {ACM},

refereed = {yes},

length = {7}

}

**inproceedings**{RISC6096,author = {David M. Cerna and Martina Seidl and Wolfgang Schreiner and Wolfgang Windsteiger and Armin Biere},

title = {{Aiding an Introduction to Formal Reasoning Within a First-Year Logic Course for CS Majors Using a Mobile Self-Study App}},

booktitle = {{ITICSE 2020}},

language = {english},

abstract = {In this paper, we share our experiences concerning the introduc-tion of the Android-based self-study app AXolotl within the first-semester logic course offered at our university. This course is manda-tory for students majoring in Computer Science and Artificial In-telligence. AXolotl was used as part of an optional lab assignmentbridging clausal reasoning and SAT solving with classical reason-ing, proof construction, and first-order logic. The app provides anintuitive interface for proof construction in various logical calculiand aids the students through rule application. The goal of thelab assignment was to help students make a smoother transitionfrom clausal and decompositional reasoning used earlier in thecourse to inferential and contextual reasoning required for proofconstruction and first-order logic. We observed that the lab had apositive influence on students’ understanding and end the paperwith a discussion of these results.},

pages = {1--7},

isbn_issn = {https://doi.org/10.1145/3341525.3387409},

year = {2020},

editor = {ACM},

refereed = {yes},

length = {7}

}

[Cerna]

### Computational Logic in the First Semester of Computer Science: An Experience Report

#### David M. Cerna and Martina Seidl and Wolfgang Schreiner and Wolfgang Windsteiger and Armin Biere

In: CSEDU 2020, Springer (ed.), pp. 1-8. 2020. not yet known.@

author = {David M. Cerna and Martina Seidl and Wolfgang Schreiner and Wolfgang Windsteiger and Armin Biere},

title = {{Computational Logic in the First Semester of Computer Science: An Experience Report}},

booktitle = {{CSEDU 2020}},

language = {english},

abstract = {Nowadays, logic plays an ever-increasing role in modern computer science, in theory as well as in practice.Logic forms the foundation of the symbolic branch of artificial intelligence and from an industrial perspective,logic-based verification technologies are crucial for major hardware and software companies to ensure thecorrectness of complex computing systems. The concepts of computational logic that are needed for such purposes are often avoided in early stages of computer science curricula. Instead, classical logic education mainlyfocuses on mathematical aspects of logic depriving students to see the practical relevance of this subject. Inthis paper we present our experiences with a novel design of a first-semester bachelor logic course attendedby about 200 students. Our aim is to interlink both foundations and applications of logic within computerscience. We report on our experiences and the feedback we got from the students through an extensive surveywe performed at the end of the semester.},

pages = {1--8},

isbn_issn = {not yet known},

year = {2020},

editor = {Springer},

refereed = {yes},

length = {8}

}

**inproceedings**{RISC6097,author = {David M. Cerna and Martina Seidl and Wolfgang Schreiner and Wolfgang Windsteiger and Armin Biere},

title = {{Computational Logic in the First Semester of Computer Science: An Experience Report}},

booktitle = {{CSEDU 2020}},

language = {english},

abstract = {Nowadays, logic plays an ever-increasing role in modern computer science, in theory as well as in practice.Logic forms the foundation of the symbolic branch of artificial intelligence and from an industrial perspective,logic-based verification technologies are crucial for major hardware and software companies to ensure thecorrectness of complex computing systems. The concepts of computational logic that are needed for such purposes are often avoided in early stages of computer science curricula. Instead, classical logic education mainlyfocuses on mathematical aspects of logic depriving students to see the practical relevance of this subject. Inthis paper we present our experiences with a novel design of a first-semester bachelor logic course attendedby about 200 students. Our aim is to interlink both foundations and applications of logic within computerscience. We report on our experiences and the feedback we got from the students through an extensive surveywe performed at the end of the semester.},

pages = {1--8},

isbn_issn = {not yet known},

year = {2020},

editor = {Springer},

refereed = {yes},

length = {8}

}

[Cerna]

### A Note on Anti-unification and the Theory of Semirings

#### David M. Cerna

RISC. Technical report, 2020. [pdf]@

author = {David M. Cerna},

title = {{A Note on Anti-unification and the Theory of Semirings}},

language = {english},

abstract = {It was recently shown that anti-unification over an equational theory consisting of only identity equations (more than one) is nullary. Such pure theories are artificial and are of little effect on practical aspects of anti-unification. In this work, we extend these nullarity results to the theory of semirings, a heavily studied theory with many practical applications. Furthermore, our argument holds over semirings with commutative multiplication and/or idempotent addition. },

year = {2020},

institution = {RISC},

length = {4}

}

**techreport**{RISC6101,author = {David M. Cerna},

title = {{A Note on Anti-unification and the Theory of Semirings}},

language = {english},

abstract = {It was recently shown that anti-unification over an equational theory consisting of only identity equations (more than one) is nullary. Such pure theories are artificial and are of little effect on practical aspects of anti-unification. In this work, we extend these nullarity results to the theory of semirings, a heavily studied theory with many practical applications. Furthermore, our argument holds over semirings with commutative multiplication and/or idempotent addition. },

year = {2020},

institution = {RISC},

length = {4}

}

[Dramnesc]

### Implementation of Deletion Algorithms on Lists and Binary Trees in Theorema

#### Isabela Dramnesc, Tudor Jebelean

Technical report no. 20-04 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. April 2020. [pdf]@

author = {Isabela Dramnesc and Tudor Jebelean},

title = {{Implementation of Deletion Algorithms on Lists and Binary Trees in Theorema}},

language = {english},

number = {20-04},

year = {2020},

month = {April},

length = {25},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

**techreport**{RISC6094,author = {Isabela Dramnesc and Tudor Jebelean},

title = {{Implementation of Deletion Algorithms on Lists and Binary Trees in Theorema}},

language = {english},

number = {20-04},

year = {2020},

month = {April},

length = {25},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

[Goswami]

### On sums of coefficients of polynomials related to the Borwein conjectures

#### Ankush Goswami, Venkata Raghu Tej Pantangi

May 2020. [pdf]@

author = {Ankush Goswami and Venkata Raghu Tej Pantangi},

title = {{On sums of coefficients of polynomials related to the Borwein conjectures}},

language = {english},

abstract = {Recently, Li (Int. J. Number Theory 2020) obtained an asymptotic formula for a certain partial sum involving coefficients for the polynomial in the First Borwein conjecture. As a consequence, he showed the positivity of this sum. His result was based on a sieving principle discovered by himself and Wan (Sci. China. Math. 2010). In fact, Li points out in his paper that his method can be generalized to prove an asymptotic formula for a general partial sum involving coefficients for any prime $p>3$. In this work, we extend Li's method to obtain asymptotic formula for several partial sums of coefficients of a very general polynomial. We find that in the special cases $p=3, 5$, the signs of these sums are consistent with the three famous Borwein conjectures. Similar sums have been studied earlier by Zaharescu (Ramanujan J. 2006) using a completely different method. We also improve on the error terms in the asymptotic formula for Li and Zaharescu. Using a recent result of Borwein (JNT 1993), we also obtain an asymptotic estimate for the maximum of the absolute value of these coefficients for primes $p=2, 3, 5, 7, 11, 13$ and for $p>15$, we obtain a lower bound on the maximum absolute value of these coefficients for sufficiently large $n$.},

year = {2020},

month = {May},

length = {13},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

**techreport**{RISC6113,author = {Ankush Goswami and Venkata Raghu Tej Pantangi},

title = {{On sums of coefficients of polynomials related to the Borwein conjectures}},

language = {english},

abstract = {Recently, Li (Int. J. Number Theory 2020) obtained an asymptotic formula for a certain partial sum involving coefficients for the polynomial in the First Borwein conjecture. As a consequence, he showed the positivity of this sum. His result was based on a sieving principle discovered by himself and Wan (Sci. China. Math. 2010). In fact, Li points out in his paper that his method can be generalized to prove an asymptotic formula for a general partial sum involving coefficients for any prime $p>3$. In this work, we extend Li's method to obtain asymptotic formula for several partial sums of coefficients of a very general polynomial. We find that in the special cases $p=3, 5$, the signs of these sums are consistent with the three famous Borwein conjectures. Similar sums have been studied earlier by Zaharescu (Ramanujan J. 2006) using a completely different method. We also improve on the error terms in the asymptotic formula for Li and Zaharescu. Using a recent result of Borwein (JNT 1993), we also obtain an asymptotic estimate for the maximum of the absolute value of these coefficients for primes $p=2, 3, 5, 7, 11, 13$ and for $p>15$, we obtain a lower bound on the maximum absolute value of these coefficients for sufficiently large $n$.},

year = {2020},

month = {May},

length = {13},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

[Goswami]

### Some formulae for coefficients in restricted $q$-products

#### Ankush Goswami, Venkata Raghu Tej Pantangi

May 2020. [pdf]@

author = {Ankush Goswami and Venkata Raghu Tej Pantangi},

title = {{Some formulae for coefficients in restricted $q$-products}},

language = {english},

abstract = {In this paper, we derive some formulae involving coefficients of polynomials which occur quite naturally in the study of restricted partitions. Our method involves a recently discovered sieve technique by Li and Wan (Sci. China. Math. 2010). Based on this method, by considering cyclic groups of different orders we obtain some new results for these coefficients. The general result (see Theorem \ref{main00}) holds for any group of the form $\mathbb{Z}_{N}$ where $N\in\mathbb{N}$ and expresses certain partial sums of coefficients in terms of expressions involving roots of unity. By specializing $N$ to different values, we see that these expressions simplify in some cases and we obtain several nice identities involving these coefficients. We also use a result of Sudler (Quarterly J. Math. 1964) to obtain an asymptotic formula for the maximum absolute value of these coefficients.},

year = {2020},

month = {May},

length = {11},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

**techreport**{RISC6114,author = {Ankush Goswami and Venkata Raghu Tej Pantangi},

title = {{Some formulae for coefficients in restricted $q$-products}},

language = {english},

abstract = {In this paper, we derive some formulae involving coefficients of polynomials which occur quite naturally in the study of restricted partitions. Our method involves a recently discovered sieve technique by Li and Wan (Sci. China. Math. 2010). Based on this method, by considering cyclic groups of different orders we obtain some new results for these coefficients. The general result (see Theorem \ref{main00}) holds for any group of the form $\mathbb{Z}_{N}$ where $N\in\mathbb{N}$ and expresses certain partial sums of coefficients in terms of expressions involving roots of unity. By specializing $N$ to different values, we see that these expressions simplify in some cases and we obtain several nice identities involving these coefficients. We also use a result of Sudler (Quarterly J. Math. 1964) to obtain an asymptotic formula for the maximum absolute value of these coefficients.},

year = {2020},

month = {May},

length = {11},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

[Grasegger]

### Graphs with Flexible Labelings allowing Injective Realizations

#### G. Grasegger, J. Legerský, J. Schicho

Discrete Mathematics 343(6), pp. Art. 111713-. 2020. ISSN 0012-365X. [url]@

author = {G. Grasegger and J. Legerský and J. Schicho},

title = {{Graphs with Flexible Labelings allowing Injective Realizations}},

language = {english},

journal = {Discrete Mathematics},

volume = {343},

number = {6},

pages = {Art. 111713--},

isbn_issn = {ISSN 0012-365X},

year = {2020},

refereed = {yes},

length = {14},

url = {https://doi.org/10.1016/j.disc.2019.111713}

}

**article**{RISC6012,author = {G. Grasegger and J. Legerský and J. Schicho},

title = {{Graphs with Flexible Labelings allowing Injective Realizations}},

language = {english},

journal = {Discrete Mathematics},

volume = {343},

number = {6},

pages = {Art. 111713--},

isbn_issn = {ISSN 0012-365X},

year = {2020},

refereed = {yes},

length = {14},

url = {https://doi.org/10.1016/j.disc.2019.111713}

}

[Grasegger]

### FlexRiLoG - A SageMath Package for Motions of Graphs

#### G. Grasegger, J. Legerský

arXiv. Technical report, 2020. [url]@

author = {G. Grasegger and J. Legerský},

title = {{FlexRiLoG - A SageMath Package for Motions of Graphs}},

language = {english},

year = {2020},

institution = {arXiv},

length = {9},

url = {https://arxiv.org/abs/2003.12029}

}

**techreport**{RISC6090,author = {G. Grasegger and J. Legerský},

title = {{FlexRiLoG - A SageMath Package for Motions of Graphs}},

language = {english},

year = {2020},

institution = {arXiv},

length = {9},

url = {https://arxiv.org/abs/2003.12029}

}

[Grasegger]

### Flexible placements of graphs with rotational symmetry

#### S.Dewar, G. Grasegger, J. Legerský

arXiv. Technical report, 2020. [url]@

author = {S.Dewar and G. Grasegger and J. Legerský},

title = {{Flexible placements of graphs with rotational symmetry}},

language = {english},

year = {2020},

institution = {arXiv},

length = {9},

url = {https://arxiv.org/abs/2003.09328}

}

**techreport**{RISC6091,author = {S.Dewar and G. Grasegger and J. Legerský},

title = {{Flexible placements of graphs with rotational symmetry}},

language = {english},

year = {2020},

institution = {arXiv},

length = {9},

url = {https://arxiv.org/abs/2003.09328}

}

[Grasegger]

### On the Classification of Motions of Paradoxically Movable Graphs

#### G. Grasegger, J. Legerský, J. Schicho

arXiv. Technical report, 2020. [url]@

author = {G. Grasegger and J. Legerský and J. Schicho},

title = {{On the Classification of Motions of Paradoxically Movable Graphs}},

language = {english},

year = {2020},

institution = {arXiv},

length = {27},

url = {https://arxiv.org/abs/2003.11416}

}

**techreport**{RISC6092,author = {G. Grasegger and J. Legerský and J. Schicho},

title = {{On the Classification of Motions of Paradoxically Movable Graphs}},

language = {english},

year = {2020},

institution = {arXiv},

length = {27},

url = {https://arxiv.org/abs/2003.11416}

}

[Grasegger]

### Combinatorics of Bricard’s octahedra

#### M. Gallet, G. Grasegger, J. Legerský, J. Schicho

arXiv. Technical report, 2020. [url]@

author = {M. Gallet and G. Grasegger and J. Legerský and J. Schicho},

title = {{Combinatorics of Bricard’s octahedra}},

language = {english},

year = {2020},

institution = {arXiv},

length = {40},

url = {https://arxiv.org/pdf/2004.01236.pdf}

}

**techreport**{RISC6095,author = {M. Gallet and G. Grasegger and J. Legerský and J. Schicho},

title = {{Combinatorics of Bricard’s octahedra}},

language = {english},

year = {2020},

institution = {arXiv},

length = {40},

url = {https://arxiv.org/pdf/2004.01236.pdf}

}

[Jimenez Pastor]

### Some structural results on D^n finite functions

#### A. Jimenez-Pastor, V. Pillwein, M.F. Singer

Advances in Applied Mathematics 117, pp. 0-0. June 2020. Elsevier, 0196-8858. [url] [pdf]@

author = {A. Jimenez-Pastor and V. Pillwein and M.F. Singer},

title = {{Some structural results on D^n finite functions}},

language = {english},

abstract = {D-finite (or holonomic) functions satisfy linear differential equations with polynomial coefficients. They form a large class of functions that appear in many applications in Mathematics or Physics. It is well-known that these functions are closed under certain operations and these closure properties can be executed algorithmically. Recently, the notion of D-finite functions has been generalized to differentially definable or Dn-finite functions. Also these functions are closed under operations such as forming (anti)derivative, addition or multiplication and, again, these can be implemented. In this paper we investigate how Dn-finite functions behave under composition and how they are related to algebraic and differentially algebraic functions.},

journal = {Advances in Applied Mathematics},

volume = {117},

pages = {0--0},

publisher = {Elsevier},

isbn_issn = {0196-8858},

year = {2020},

month = {June},

refereed = {yes},

length = {0},

url = {https://doi.org/10.1016/j.aam.2020.102027}

}

**article**{RISC6077,author = {A. Jimenez-Pastor and V. Pillwein and M.F. Singer},

title = {{Some structural results on D^n finite functions}},

language = {english},

abstract = {D-finite (or holonomic) functions satisfy linear differential equations with polynomial coefficients. They form a large class of functions that appear in many applications in Mathematics or Physics. It is well-known that these functions are closed under certain operations and these closure properties can be executed algorithmically. Recently, the notion of D-finite functions has been generalized to differentially definable or Dn-finite functions. Also these functions are closed under operations such as forming (anti)derivative, addition or multiplication and, again, these can be implemented. In this paper we investigate how Dn-finite functions behave under composition and how they are related to algebraic and differentially algebraic functions.},

journal = {Advances in Applied Mathematics},

volume = {117},

pages = {0--0},

publisher = {Elsevier},

isbn_issn = {0196-8858},

year = {2020},

month = {June},

refereed = {yes},

length = {0},

url = {https://doi.org/10.1016/j.aam.2020.102027}

}

[Kutsia]

### Unification modulo alpha-equivalence in a mathematical assistant system

#### Temur Kutsia

Technical report no. 20-01 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 2020. [pdf]@

author = {Temur Kutsia},

title = {{Unification modulo alpha-equivalence in a mathematical assistant system}},

language = {english},

number = {20-01},

year = {2020},

length = {21},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

**techreport**{RISC6074,author = {Temur Kutsia},

title = {{Unification modulo alpha-equivalence in a mathematical assistant system}},

language = {english},

number = {20-01},

year = {2020},

length = {21},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

[Paule]

### Holonomic Relations for Modular Functions and Forms: First Guess, then Prove

#### Peter Paule, Silviu Radu

2020. [pdf]@

author = {Peter Paule and Silviu Radu},

title = {{Holonomic Relations for Modular Functions and Forms: First Guess, then Prove}},

language = {english},

year = {2020},

length = {46},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

**techreport**{RISC6081,author = {Peter Paule and Silviu Radu},

title = {{Holonomic Relations for Modular Functions and Forms: First Guess, then Prove}},

language = {english},

year = {2020},

length = {46},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

[Paule]

### An algorithm to prove holonomic differential equations for modular forms

#### Peter Paule, Cristian-Silviu Radu

May 2020. [pdf]@

author = {Peter Paule and Cristian-Silviu Radu},

title = {{An algorithm to prove holonomic differential equations for modular forms}},

language = {english},

abstract = {Express a modular form $g$ of positive weight locally in terms of a modular function $h$ as$y(h)$, say. Then $y(h)$ as a function in $h$ satisfiesa holonomic differential equation; i.e., one which islinear with coefficients being polynomials in $h$.This fact traces back to Gau{\ss} and has beenpopularized prominently by Zagier. Using holonomicprocedures, computationally it is often straightforwardto derive such differential equations as conjectures.In the spirit of the ``first guess, then prove'' paradigm,we present a new algorithm to prove such conjectures.},

year = {2020},

month = {May},

keywords = {modular functions, modular forms, holonomic differential equations, holonomic functions and sequences, Fricke-Klein relations, $q$-series, partition congruences},

sponsor = {FWF SFB F50},

length = {48},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

**techreport**{RISC6108,author = {Peter Paule and Cristian-Silviu Radu},

title = {{An algorithm to prove holonomic differential equations for modular forms}},

language = {english},

abstract = {Express a modular form $g$ of positive weight locally in terms of a modular function $h$ as$y(h)$, say. Then $y(h)$ as a function in $h$ satisfiesa holonomic differential equation; i.e., one which islinear with coefficients being polynomials in $h$.This fact traces back to Gau{\ss} and has beenpopularized prominently by Zagier. Using holonomicprocedures, computationally it is often straightforwardto derive such differential equations as conjectures.In the spirit of the ``first guess, then prove'' paradigm,we present a new algorithm to prove such conjectures.},

year = {2020},

month = {May},

keywords = {modular functions, modular forms, holonomic differential equations, holonomic functions and sequences, Fricke-Klein relations, $q$-series, partition congruences},

sponsor = {FWF SFB F50},

length = {48},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

[Pillwein]

### A sequence of polynomials generated by a Kapteyn series of the second kind

#### D. Dominici, V. Pillwein

In: Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra, in Honour of Peter Paule on his 60th Birthday, V. Pillwein and C. Schneider (ed.), Texts and Monographs in Symbolic Computuation, in press , pp. ?-?. 2020. Springer, arXiv:1607.05314 [math.CO]. [url] [pdf]@

author = {D. Dominici and V. Pillwein},

title = {{A sequence of polynomials generated by a Kapteyn series of the second kind}},

booktitle = {{Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra, in Honour of Peter Paule on his 60th Birthday}},

language = {english},

series = {Texts and Monographs in Symbolic Computuation, in press},

pages = {?--?},

publisher = {Springer},

isbn_issn = {?},

year = {2020},

note = {arXiv:1607.05314 [math.CO]},

editor = {V. Pillwein and C. Schneider},

refereed = {yes},

length = {0},

url = {https://www.dk-compmath.jku.at/publications/dk-reports/2019-05-28/view}

}

**incollection**{RISC6078,author = {D. Dominici and V. Pillwein},

title = {{A sequence of polynomials generated by a Kapteyn series of the second kind}},

booktitle = {{Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra, in Honour of Peter Paule on his 60th Birthday}},

language = {english},

series = {Texts and Monographs in Symbolic Computuation, in press},

pages = {?--?},

publisher = {Springer},

isbn_issn = {?},

year = {2020},

note = {arXiv:1607.05314 [math.CO]},

editor = {V. Pillwein and C. Schneider},

refereed = {yes},

length = {0},

url = {https://www.dk-compmath.jku.at/publications/dk-reports/2019-05-28/view}

}

[Radu]

### A Reduction Theorem of Certain Relations Modulo p Involving Modular Forms

#### Radu, Cristian-Silviu

In: Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra, in Honour of Peter Paule on his 60th Birthday, V. Pillwein, C. Schneider (ed.), pp. 1-15. 2020. Springer, 978-3-030-44558-4. [pdf]@

author = {Radu and Cristian-Silviu},

title = {{A Reduction Theorem of Certain Relations Modulo p Involving Modular Forms}},

booktitle = {{Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra, in Honour of Peter Paule on his 60th Birthday}},

language = {english},

pages = {1--15},

publisher = {Springer},

isbn_issn = {978-3-030-44558-4},

year = {2020},

editor = {V. Pillwein and C. Schneider},

refereed = {yes},

length = {15}

}

**incollection**{RISC6110,author = {Radu and Cristian-Silviu},

title = {{A Reduction Theorem of Certain Relations Modulo p Involving Modular Forms}},

booktitle = {{Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra, in Honour of Peter Paule on his 60th Birthday}},

language = {english},

pages = {1--15},

publisher = {Springer},

isbn_issn = {978-3-030-44558-4},

year = {2020},

editor = {V. Pillwein and C. Schneider},

refereed = {yes},

length = {15}

}