# Computer Algebra Algorithms for q-Series and Combinatorial Identities

### Project Lead

### Project Duration

01/10/1989 - 31/03/1993## Partners

### The Austrian Science Fund (FWF)

## Publications

### 2022

[Banerjee]

### Hook Type enumeration and parity of parts in partitions

#### K. Banerjee, M. G. Dastidar

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6596, 2022. [pdf]@

author = {K. Banerjee and M. G. Dastidar},

title = {{Hook Type enumeration and parity of parts in partitions}},

language = {english},

abstract = {This paper is devoted to study an association between hook type enumeration and counting integer partitions subject to parity of its parts. We shall primarily focus on a result of Andrews in two possible direction. First, we confirm a conjecture of Rubey and secondly, we extend the theorem of Andrews in a more general set up. },

number = {RISC6596},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {8}

}

**techreport**{RISC6596,author = {K. Banerjee and M. G. Dastidar},

title = {{Hook Type enumeration and parity of parts in partitions}},

language = {english},

abstract = {This paper is devoted to study an association between hook type enumeration and counting integer partitions subject to parity of its parts. We shall primarily focus on a result of Andrews in two possible direction. First, we confirm a conjecture of Rubey and secondly, we extend the theorem of Andrews in a more general set up. },

number = {RISC6596},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {8}

}

[Banerjee]

### Hook type tableaux and partition identities

#### K. Banerjee, M. G. Dastidar

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6597, 2022. [pdf]@

author = {K. Banerjee and M. G. Dastidar},

title = {{Hook type tableaux and partition identities}},

language = {english},

abstract = {In this paper we exhibit the box-stacking principle (BSP) in conjunction with Young diagrams to prove generalizations of Stanley's and Elder's theorems without even the use of partition statistics in general. We primarily focus on to study Stanley's theorem in color partition context.},

number = {RISC6597},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {13}

}

**techreport**{RISC6597,author = {K. Banerjee and M. G. Dastidar},

title = {{Hook type tableaux and partition identities}},

language = {english},

abstract = {In this paper we exhibit the box-stacking principle (BSP) in conjunction with Young diagrams to prove generalizations of Stanley's and Elder's theorems without even the use of partition statistics in general. We primarily focus on to study Stanley's theorem in color partition context.},

number = {RISC6597},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {13}

}

[Banerjee]

### Positivity of the second shifted difference of partitions and overpartitions: a combinatorial approach

#### Koustav Banerjee

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6592, 2022. [pdf]@

author = {Koustav Banerjee},

title = {{Positivity of the second shifted difference of partitions and overpartitions: a combinatorial approach}},

language = {english},

number = {RISC6592},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {5}

}

**techreport**{RISC6592,author = {Koustav Banerjee},

title = {{Positivity of the second shifted difference of partitions and overpartitions: a combinatorial approach}},

language = {english},

number = {RISC6592},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {5}

}

[Banerjee]

### Ramanujan's theta functions and parity of parts and cranks of partitions

#### K. Banerjee, M. G. Dastidar

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6595, 2022. [pdf]@

author = {K. Banerjee and M. G. Dastidar},

title = {{Ramanujan's theta functions and parity of parts and cranks of partitions}},

language = {english},

abstract = {In this paper we explore intricate connections between Ramanujan's theta functions and a class of partition functions defined by the nature of the parity of their parts. This consequently leads us to the parity analysis of the crank of a partition and its correlation to the number of partitions with odd number of parts, self-conjugate partitions, and also with Durfee squares and Frobenius symbols.},

number = {RISC6595},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {13}

}

**techreport**{RISC6595,author = {K. Banerjee and M. G. Dastidar},

title = {{Ramanujan's theta functions and parity of parts and cranks of partitions}},

language = {english},

abstract = {In this paper we explore intricate connections between Ramanujan's theta functions and a class of partition functions defined by the nature of the parity of their parts. This consequently leads us to the parity analysis of the crank of a partition and its correlation to the number of partitions with odd number of parts, self-conjugate partitions, and also with Durfee squares and Frobenius symbols.},

number = {RISC6595},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {13}

}

[Banerjee]

### Inequalities for the partition function arising from truncated theta series

#### K. Banerjee, M. G. Dastidar

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6622, 2022. [pdf]@

author = {K. Banerjee and M. G. Dastidar},

title = {{Inequalities for the partition function arising from truncated theta series}},

language = {english},

number = {RISC6622},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {12}

}

**techreport**{RISC6622,author = {K. Banerjee and M. G. Dastidar},

title = {{Inequalities for the partition function arising from truncated theta series}},

language = {english},

number = {RISC6622},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {12}

}

[Banerjee]

### Parity biases in partitions and restricted partitions

#### Banerjee Koustav, Bhattacharjee Sreerupa, Dastidar Manosij Ghosh, Mahanta Pankaj Jyoti, Saikia Manjil P

European Journal of Combinatorics 103, pp. 103522-103522. 2022. Elsevier, ISSN 0195-6698. [pdf]@

author = {Banerjee Koustav and Bhattacharjee Sreerupa and Dastidar Manosij Ghosh and Mahanta Pankaj Jyoti and Saikia Manjil P},

title = {{Parity biases in partitions and restricted partitions}},

language = {english},

journal = {European Journal of Combinatorics},

volume = {103},

pages = {103522--103522},

publisher = {Elsevier},

isbn_issn = {ISSN 0195-6698},

year = {2022},

refereed = {yes},

length = {19}

}

**article**{RISC6606,author = {Banerjee Koustav and Bhattacharjee Sreerupa and Dastidar Manosij Ghosh and Mahanta Pankaj Jyoti and Saikia Manjil P},

title = {{Parity biases in partitions and restricted partitions}},

language = {english},

journal = {European Journal of Combinatorics},

volume = {103},

pages = {103522--103522},

publisher = {Elsevier},

isbn_issn = {ISSN 0195-6698},

year = {2022},

refereed = {yes},

length = {19}

}

[Banerjee]

### New inequalities for p(n) and log p(n)

#### K. Banerjee, P. Paule, C. S. Radu, W. H. Zeng

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6607, 2022. [pdf]@

author = {K. Banerjee and P. Paule and C. S. Radu and W. H. Zeng},

title = {{New inequalities for p(n) and log p(n)}},

language = {english},

number = {RISC6607},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {37}

}

**techreport**{RISC6607,author = {K. Banerjee and P. Paule and C. S. Radu and W. H. Zeng},

title = {{New inequalities for p(n) and log p(n)}},

language = {english},

number = {RISC6607},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {37}

}

[Banerjee]

### Inequalities for the modified Bessel function of first kind of non-negative order

#### K. Banerjee

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6608, 2022. [pdf]@

author = {K. Banerjee},

title = {{Inequalities for the modified Bessel function of first kind of non-negative order}},

language = {english},

number = {RISC6608},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {28}

}

**techreport**{RISC6608,author = {K. Banerjee},

title = {{Inequalities for the modified Bessel function of first kind of non-negative order}},

language = {english},

number = {RISC6608},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {28}

}

[Banerjee]

### An unified framework to prove multiplicative inequalities for the partition function

#### K. Banerjee

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6614, 2022. [pdf]@

author = {K. Banerjee},

title = {{An unified framework to prove multiplicative inequalities for the partition function}},

language = {english},

number = {RISC6614},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {24}

}

**techreport**{RISC6614,author = {K. Banerjee},

title = {{An unified framework to prove multiplicative inequalities for the partition function}},

language = {english},

number = {RISC6614},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {24}

}

[Banerjee]

### The localization method applied to k-elognated plane partitions and divisibily by 5

#### K. Banerjee, N. A. Smoot

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6611, 2022. [pdf]@

author = {K. Banerjee and N. A. Smoot},

title = {{The localization method applied to k-elognated plane partitions and divisibily by 5}},

language = {english},

number = {RISC6611},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {40}

}

**techreport**{RISC6611,author = {K. Banerjee and N. A. Smoot},

title = {{The localization method applied to k-elognated plane partitions and divisibily by 5}},

language = {english},

number = {RISC6611},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {40}

}

[Banerjee]

### Invariants of the quartic binary form and proofs of Chen's conjectures on partition function inequalities

#### K. Banerjee

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6615, 2022. [pdf]@

author = {K. Banerjee},

title = {{Invariants of the quartic binary form and proofs of Chen's conjectures on partition function inequalities}},

language = {english},

number = {RISC6615},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {31}

}

**techreport**{RISC6615,author = {K. Banerjee},

title = {{Invariants of the quartic binary form and proofs of Chen's conjectures on partition function inequalities}},

language = {english},

number = {RISC6615},

year = {2022},

institution = {Research Institute for Symbolic Computation, JKU, Linz},

length = {31}

}

[Dominici]

### Truncated Hermite polynomials

#### Diego Dominici and Francisco Marcell{\'a}n

Technical report no. 22-10 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). August 2022. Licensed under CC BY 4.0 International. [doi] [pdf]@

author = {Diego Dominici and Francisco Marcell{\'a}n},

title = {{Truncated Hermite polynomials}},

language = {english},

abstract = {We define the family of truncated Hermite polynomials $P_{n}left(x;zright) $, orthogonal with respect to the linear functional[Lleft[ pright] = int_{-z}^{z} pleft( xright) e^{-x^{2}} ,dx. ]The connection of $P_{n}left( x;zright) $ with the Hermite and Rys polynomialsis stated. The semiclassical character of $P_{n}left( x;zright) $ aspolynomials of class $2$ is emphasized.As a consequence, several properties of $P_{n}left( x;zright) $ concerningthe coefficients $gamma_{n}left( zright) $ in the three-term recurrencerelation they satisfy as well as the moments and the Stieltjes function of $L$are given. Ladder operators associated with the linear functional $L$, aholonomic differential equation (in $x)$ for the polynomials $P_{n}left(x;zright) $, and a nonlinear ODE for the functions $gamma_{n}left(zright) $ are deduced. },

number = {22-10},

year = {2022},

month = {August},

keywords = {Orthogonal polynomials, Gaussian distribution},

length = {37},

license = {CC BY 4.0 International},

type = {RISC Report Series},

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

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}

**techreport**{RISC6531,author = {Diego Dominici and Francisco Marcell{\'a}n},

title = {{Truncated Hermite polynomials}},

language = {english},

abstract = {We define the family of truncated Hermite polynomials $P_{n}left(x;zright) $, orthogonal with respect to the linear functional[Lleft[ pright] = int_{-z}^{z} pleft( xright) e^{-x^{2}} ,dx. ]The connection of $P_{n}left( x;zright) $ with the Hermite and Rys polynomialsis stated. The semiclassical character of $P_{n}left( x;zright) $ aspolynomials of class $2$ is emphasized.As a consequence, several properties of $P_{n}left( x;zright) $ concerningthe coefficients $gamma_{n}left( zright) $ in the three-term recurrencerelation they satisfy as well as the moments and the Stieltjes function of $L$are given. Ladder operators associated with the linear functional $L$, aholonomic differential equation (in $x)$ for the polynomials $P_{n}left(x;zright) $, and a nonlinear ODE for the functions $gamma_{n}left(zright) $ are deduced. },

number = {22-10},

year = {2022},

month = {August},

keywords = {Orthogonal polynomials, Gaussian distribution},

length = {37},

license = {CC BY 4.0 International},

type = {RISC Report Series},

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

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}

[Dominici]

### Comparative asymptotics for discrete semiclassical orthogonal polynomials

#### Diego Dominici

Technical report no. 22-11 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). August 2022. Licensed under CC BY 4.0 International. [doi] [pdf]@

author = {Diego Dominici},

title = {{Comparative asymptotics for discrete semiclassical orthogonal polynomials}},

language = {english},

abstract = {We study the ratio $frac{P_{n}left( x;zright) }{phi_{n}left( xright)}$ asymptotically as $nrightarrowinfty,$ where the polynomials $P_{n}left(x;zright) $ are orthogonal with respect to a discrete linear functional and$phi_{n}left( xright) $ denote the falling factorial polynomials.We give recurrences that allow the computation of high order asymptoticexpansions of $P_{n}left( x;zright) $ and give examples for most discretesemiclassical polynomials of class $sleq2.$We show several plots illustrating the accuracy of our results.},

number = {22-11},

year = {2022},

month = {August},

keywords = {Orthogonal polynomials, asymptotic analysis },

length = {53},

license = {CC BY 4.0 International},

type = {RISC Report Series},

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

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}

**techreport**{RISC6579,author = {Diego Dominici},

title = {{Comparative asymptotics for discrete semiclassical orthogonal polynomials}},

language = {english},

abstract = {We study the ratio $frac{P_{n}left( x;zright) }{phi_{n}left( xright)}$ asymptotically as $nrightarrowinfty,$ where the polynomials $P_{n}left(x;zright) $ are orthogonal with respect to a discrete linear functional and$phi_{n}left( xright) $ denote the falling factorial polynomials.We give recurrences that allow the computation of high order asymptoticexpansions of $P_{n}left( x;zright) $ and give examples for most discretesemiclassical polynomials of class $sleq2.$We show several plots illustrating the accuracy of our results.},

number = {22-11},

year = {2022},

month = {August},

keywords = {Orthogonal polynomials, asymptotic analysis },

length = {53},

license = {CC BY 4.0 International},

type = {RISC Report Series},

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

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}

[Dundua]

### Unranked Nominal Unification

#### Besik Dundua, Temur Kutsia, Mikheil Rukhaia

In: Proceedings of TbiLLC 2019 - 13th International Tbilisi Symposium on Logic, Language, and Computation, Aybüke Özgün and Yulia Zinova (ed.), Proceedings of 13th International Tbilisi Symposium on Logic, Language, and Computation, Lecture Notes in Computer Science 13206, pp. 279-296. 2022. Springer, ISBN 978-3-030-98478-6. [doi] [pdf]@

author = {Besik Dundua and Temur Kutsia and Mikheil Rukhaia},

title = {{Unranked Nominal Unification}},

booktitle = {{Proceedings of TbiLLC 2019 - 13th International Tbilisi Symposium on Logic, Language, and Computation}},

language = {english},

series = {Lecture Notes in Computer Science},

volume = {13206},

pages = {279--296},

publisher = {Springer},

isbn_issn = {ISBN 978-3-030-98478-6},

year = {2022},

editor = {Aybüke Özgün and Yulia Zinova},

refereed = {yes},

length = {17},

conferencename = {13th International Tbilisi Symposium on Logic, Language, and Computation},

url = {https://doi.org/10.1007/978-3-030-98479-3_14}

}

**inproceedings**{RISC6498,author = {Besik Dundua and Temur Kutsia and Mikheil Rukhaia},

title = {{Unranked Nominal Unification}},

booktitle = {{Proceedings of TbiLLC 2019 - 13th International Tbilisi Symposium on Logic, Language, and Computation}},

language = {english},

series = {Lecture Notes in Computer Science},

volume = {13206},

pages = {279--296},

publisher = {Springer},

isbn_issn = {ISBN 978-3-030-98478-6},

year = {2022},

editor = {Aybüke Özgün and Yulia Zinova},

refereed = {yes},

length = {17},

conferencename = {13th International Tbilisi Symposium on Logic, Language, and Computation},

url = {https://doi.org/10.1007/978-3-030-98479-3_14}

}

[Falkensteiner]

### On Initials and the Fundamental Theorem of Tropical Partial Differential Geometry

#### S. Falkensteiner, C. Garay-Lopez, M. Haiech, M. P. Noordman, F. Boulier, Z. Toghani

Journal of Symbolic Computation 115, pp. 53-73. 2022. ISSN: 0747-7171. [doi]@

author = {S. Falkensteiner and C. Garay-Lopez and M. Haiech and M. P. Noordman and F. Boulier and Z. Toghani},

title = {{On Initials and the Fundamental Theorem of Tropical Partial Differential Geometry}},

language = {english},

journal = {Journal of Symbolic Computation},

volume = {115},

pages = {53--73},

isbn_issn = {ISSN: 0747-7171},

year = {2022},

refereed = {yes},

keywords = {Differential Algebra, Tropical Differential Algebraic Geometry, Power Series Solutions, Newton Polyhedra, Arc Spaces, Tropical Differential Equations, Initial forms of Differential Polynomials},

length = {21},

url = {https://doi.org/10.1016/j.jsc.2022.08.005}

}

**article**{RISC6335,author = {S. Falkensteiner and C. Garay-Lopez and M. Haiech and M. P. Noordman and F. Boulier and Z. Toghani},

title = {{On Initials and the Fundamental Theorem of Tropical Partial Differential Geometry}},

language = {english},

journal = {Journal of Symbolic Computation},

volume = {115},

pages = {53--73},

isbn_issn = {ISSN: 0747-7171},

year = {2022},

refereed = {yes},

keywords = {Differential Algebra, Tropical Differential Algebraic Geometry, Power Series Solutions, Newton Polyhedra, Arc Spaces, Tropical Differential Equations, Initial forms of Differential Polynomials},

length = {21},

url = {https://doi.org/10.1016/j.jsc.2022.08.005}

}

[Falkensteiner]

### On Formal Power Series Solutions of Algebraic Ordinary Differential Equations

#### S. Falkensteiner, Yi Zhang, N. Thieu Vo

Mediterranean Journal of Mathematics 19(74), pp. 1-16. March 2022. ISSN 1660-5446. [doi]@

author = {S. Falkensteiner and Yi Zhang and N. Thieu Vo},

title = {{On Formal Power Series Solutions of Algebraic Ordinary Differential Equations}},

language = {english},

journal = {Mediterranean Journal of Mathematics},

volume = {19},

number = {74},

pages = {1--16},

isbn_issn = {ISSN 1660-5446},

year = {2022},

month = {March},

refereed = {yes},

keywords = {Formal power series, algebraic differential equation.},

length = {16},

url = {https://doi.org/10.1007/s00009-022-01984-w}

}

**article**{RISC6490,author = {S. Falkensteiner and Yi Zhang and N. Thieu Vo},

title = {{On Formal Power Series Solutions of Algebraic Ordinary Differential Equations}},

language = {english},

journal = {Mediterranean Journal of Mathematics},

volume = {19},

number = {74},

pages = {1--16},

isbn_issn = {ISSN 1660-5446},

year = {2022},

month = {March},

refereed = {yes},

keywords = {Formal power series, algebraic differential equation.},

length = {16},

url = {https://doi.org/10.1007/s00009-022-01984-w}

}

[Falkensteiner]

### Puiseux Series Solutions with Real or Rational Coefficients of First Order Autonomous AODEs

#### S. Falkensteiner

In: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, Amir Hashemi (ed.), Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC), ISSAC '22 , pp. 63-71. 2022. Association for Computing Machinery, ISBN 9781450386883. [doi]@

author = {S. Falkensteiner},

title = {{Puiseux Series Solutions with Real or Rational Coefficients of First Order Autonomous AODEs}},

booktitle = {{Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation}},

language = {english},

series = {ISSAC '22},

pages = {63--71},

publisher = {Association for Computing Machinery},

isbn_issn = {ISBN 9781450386883},

year = {2022},

editor = {Amir Hashemi},

refereed = {yes},

length = {9},

conferencename = {International Symposium on Symbolic and Algebraic Computation (ISSAC)},

url = {https://doi.org/10.1145/3476446.3536185}

}

**inproceedings**{RISC6585,author = {S. Falkensteiner},

title = {{Puiseux Series Solutions with Real or Rational Coefficients of First Order Autonomous AODEs}},

booktitle = {{Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation}},

language = {english},

series = {ISSAC '22},

pages = {63--71},

publisher = {Association for Computing Machinery},

isbn_issn = {ISBN 9781450386883},

year = {2022},

editor = {Amir Hashemi},

refereed = {yes},

length = {9},

conferencename = {International Symposium on Symbolic and Algebraic Computation (ISSAC)},

url = {https://doi.org/10.1145/3476446.3536185}

}

[Grasegger]

### Flexible placements of graphs with rotational symmetry

#### Sean Dewar, Georg Grasegger, Jan Legerský

In: 2nd IMA Conference on Mathematics of Robotics, W. Holderbaum, J.M. Selig (ed.), Springer Proceedings in Advanced Robotics 21, pp. 89-97. 2022. 978-3-030-91351-9. [doi]@

author = {Sean Dewar and Georg Grasegger and Jan Legerský},

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

booktitle = {{2nd IMA Conference on Mathematics of Robotics}},

language = {english},

series = {Springer Proceedings in Advanced Robotics},

volume = {21},

pages = {89--97},

isbn_issn = {978-3-030-91351-9},

year = {2022},

editor = {W. Holderbaum and J.M. Selig},

refereed = {yes},

length = {9},

url = {https://doi.org/10.1007/978-3-030-91352-6_9}

}

**inproceedings**{RISC6387,author = {Sean Dewar and Georg Grasegger and Jan Legerský},

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

booktitle = {{2nd IMA Conference on Mathematics of Robotics}},

language = {english},

series = {Springer Proceedings in Advanced Robotics},

volume = {21},

pages = {89--97},

isbn_issn = {978-3-030-91351-9},

year = {2022},

editor = {W. Holderbaum and J.M. Selig},

refereed = {yes},

length = {9},

url = {https://doi.org/10.1007/978-3-030-91352-6_9}

}

[Grasegger]

### Zero-Sum Cycles in Flexible Non-triangular Polyhedra

#### Matteo Gallet, Georg Grasegger, Jan Legerský, Josef Schicho

In: 2nd IMA Conference on Mathematics of Robotics, W. Holderbaum, J.M. Selig (ed.), Springer Proceedings in Advanced Robotics 21, pp. 137-143. 2022. 978-3-030-91351-9. [doi]@

author = {Matteo Gallet and Georg Grasegger and Jan Legerský and Josef Schicho},

title = {{Zero-Sum Cycles in Flexible Non-triangular Polyhedra}},

booktitle = {{2nd IMA Conference on Mathematics of Robotics}},

language = {english},

series = {Springer Proceedings in Advanced Robotics},

volume = {21},

pages = {137--143},

isbn_issn = {978-3-030-91351-9},

year = {2022},

editor = {W. Holderbaum and J.M. Selig},

refereed = {yes},

length = {7},

url = {https://doi.org/10.1007/978-3-030-91352-6_14}

}

**inproceedings**{RISC6388,author = {Matteo Gallet and Georg Grasegger and Jan Legerský and Josef Schicho},

title = {{Zero-Sum Cycles in Flexible Non-triangular Polyhedra}},

booktitle = {{2nd IMA Conference on Mathematics of Robotics}},

language = {english},

series = {Springer Proceedings in Advanced Robotics},

volume = {21},

pages = {137--143},

isbn_issn = {978-3-030-91351-9},

year = {2022},

editor = {W. Holderbaum and J.M. Selig},

refereed = {yes},

length = {7},

url = {https://doi.org/10.1007/978-3-030-91352-6_14}

}

[Kutsia]

### Nominal Unification and Matching of Higher Order Expressions with Recursive Let

#### Manfred Schmidt-Schauß, Temur Kutsia, Jordi Levy, Mateu Villaret, Yunus Kutz

Fundamenta Informaticae 185(3), pp. 247-283. 2022. IOS Press, ISSN 1875-8681. [url]@

author = {Manfred Schmidt-Schauß and Temur Kutsia and Jordi Levy and Mateu Villaret and Yunus Kutz},

title = {{Nominal Unification and Matching of Higher Order Expressions with Recursive Let}},

language = {english},

journal = {Fundamenta Informaticae},

volume = {185},

number = {3},

pages = {247--283},

publisher = {IOS Press},

isbn_issn = {ISSN 1875-8681},

year = {2022},

refereed = {yes},

length = {37},

url = {https://arxiv.org/abs/2102.08146v4}

}

**article**{RISC6506,author = {Manfred Schmidt-Schauß and Temur Kutsia and Jordi Levy and Mateu Villaret and Yunus Kutz},

title = {{Nominal Unification and Matching of Higher Order Expressions with Recursive Let}},

language = {english},

journal = {Fundamenta Informaticae},

volume = {185},

number = {3},

pages = {247--283},

publisher = {IOS Press},

isbn_issn = {ISSN 1875-8681},

year = {2022},

refereed = {yes},

length = {37},

url = {https://arxiv.org/abs/2102.08146v4}

}