# MATH LP (LIT Project)

### Project Lead

### Project Duration

01/08/2020 - 31/07/2022## Partners

### JKU

## Publications

### 2020

[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}

}

[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}

}

[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}

}

[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}

}

[Schicho]

### Probabilities of incidence between lines and a plane curve over finite field

#### M. Gallet, M. Makhul, J. Schicho

Finite Fields and Their Applications 61, pp. 1-22. 2020. 1071-5797.@

author = {M. Gallet and M. Makhul and J. Schicho},

title = {{Probabilities of incidence between lines and a plane curve over finite field}},

language = {english},

journal = {Finite Fields and Their Applications},

volume = {61},

pages = {1--22},

isbn_issn = {1071-5797},

year = {2020},

refereed = {yes},

length = {22}

}

**article**{RISC6073,author = {M. Gallet and M. Makhul and J. Schicho},

title = {{Probabilities of incidence between lines and a plane curve over finite field}},

language = {english},

journal = {Finite Fields and Their Applications},

volume = {61},

pages = {1--22},

isbn_issn = {1071-5797},

year = {2020},

refereed = {yes},

length = {22}

}

[Schneider]

### Evaluation of binomial double sums involving absolute values

#### C. Krattenthaler, C. Schneider

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

author = {C. Krattenthaler and C. Schneider},

title = {{Evaluation of binomial double sums involving absolute values}},

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 = {36},

url = {https://arxiv.org/abs/1607.05314}

}

**incollection**{RISC5970,author = {C. Krattenthaler and C. Schneider},

title = {{Evaluation of binomial double sums involving absolute values}},

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 = {36},

url = {https://arxiv.org/abs/1607.05314}

}

[Schneider]

### Minimal representations and algebraic relations for single nested products

#### C. Schneider

Programming and Computer Software 46(2), pp. 133-161. 2020. ISSN 1608-3261. arXiv:1911.04837 [cs.SC]. [url]@

author = {C. Schneider},

title = {{Minimal representations and algebraic relations for single nested products}},

language = {english},

journal = {Programming and Computer Software},

volume = {46},

number = {2},

pages = {133--161},

isbn_issn = {ISSN 1608-3261},

year = {2020},

note = {arXiv:1911.04837 [cs.SC]},

refereed = {yes},

length = {29},

url = {https://arxiv.org/abs/1911.04837}

}

**article**{RISC6002,author = {C. Schneider},

title = {{Minimal representations and algebraic relations for single nested products}},

language = {english},

journal = {Programming and Computer Software},

volume = {46},

number = {2},

pages = {133--161},

isbn_issn = {ISSN 1608-3261},

year = {2020},

note = {arXiv:1911.04837 [cs.SC]},

refereed = {yes},

length = {29},

url = {https://arxiv.org/abs/1911.04837}

}

[Schneider]

### Three loop QCD corrections to heavy quark form factors

#### J. Ablinger, J. Blümlein, P. Marquard, N. Rana, C. Schneider

In: Proceedings of ACAT 2019, to appear, pp. -. 2020. arXiv:1905.03728 [hep-ph]. [url]@

author = {J. Ablinger and J. Blümlein and P. Marquard and N. Rana and C. Schneider},

title = {{Three loop QCD corrections to heavy quark form factors}},

booktitle = {{Proceedings of ACAT 2019}},

language = {english},

volume = {to appear},

pages = {--},

isbn_issn = {?},

year = {2020},

note = {arXiv:1905.03728 [hep-ph]},

editor = {?},

refereed = {no},

length = {9},

url = {https://arxiv.org/abs/1905.03728}

}

**inproceedings**{RISC6004,author = {J. Ablinger and J. Blümlein and P. Marquard and N. Rana and C. Schneider},

title = {{Three loop QCD corrections to heavy quark form factors}},

booktitle = {{Proceedings of ACAT 2019}},

language = {english},

volume = {to appear},

pages = {--},

isbn_issn = {?},

year = {2020},

note = {arXiv:1905.03728 [hep-ph]},

editor = {?},

refereed = {no},

length = {9},

url = {https://arxiv.org/abs/1905.03728}

}

[Schneider]

### From Momentum Expansions to Post-Minkowskian Hamiltonians by Computer Algebra Algorithms

#### J. Blümlein, A. Maier, P. Marquard, G. Schäfer, C. Schneider

Physics Letters B 801(135157), pp. 1-8. 2020. ISSN 0370-2693. arXiv:1911.04411 [gr-qc]. [url]@

author = {J. Blümlein and A. Maier and P. Marquard and G. Schäfer and C. Schneider},

title = {{From Momentum Expansions to Post-Minkowskian Hamiltonians by Computer Algebra Algorithms}},

language = {english},

journal = {Physics Letters B},

volume = {801},

number = {135157},

pages = {1--8},

isbn_issn = {ISSN 0370-2693},

year = {2020},

note = {arXiv:1911.04411 [gr-qc]},

refereed = {yes},

length = {8},

url = {https://doi.org/10.1016/j.physletb.2019.135157}

}

**article**{RISC6009,author = {J. Blümlein and A. Maier and P. Marquard and G. Schäfer and C. Schneider},

title = {{From Momentum Expansions to Post-Minkowskian Hamiltonians by Computer Algebra Algorithms}},

language = {english},

journal = {Physics Letters B},

volume = {801},

number = {135157},

pages = {1--8},

isbn_issn = {ISSN 0370-2693},

year = {2020},

note = {arXiv:1911.04411 [gr-qc]},

refereed = {yes},

length = {8},

url = {https://doi.org/10.1016/j.physletb.2019.135157}

}

[Schneider]

### Heavy quark form factors at three loops

#### J. Blümlein, P. Marquard, N. Rana, C. Schneider

In: 14th International Symposium on Radiative Corrections (RADCOR2019), D. Kosower, M. Cacciari (ed.)POS(RADCOR2019)013, pp. 1-7. 2020. ISSN 1824-8039. [url]@

author = {J. Blümlein and P. Marquard and N. Rana and C. Schneider},

title = {{Heavy quark form factors at three loops}},

booktitle = {{14th International Symposium on Radiative Corrections (RADCOR2019)}},

language = {english},

volume = {POS(RADCOR2019)013},

pages = {1--7},

isbn_issn = {ISSN 1824-8039},

year = {2020},

editor = {D. Kosower and M. Cacciari},

refereed = {yes},

length = {7},

url = {https://doi.org/10.22323/1.375.0013 }

}

**inproceedings**{RISC6014,author = {J. Blümlein and P. Marquard and N. Rana and C. Schneider},

title = {{Heavy quark form factors at three loops}},

booktitle = {{14th International Symposium on Radiative Corrections (RADCOR2019)}},

language = {english},

volume = {POS(RADCOR2019)013},

pages = {1--7},

isbn_issn = {ISSN 1824-8039},

year = {2020},

editor = {D. Kosower and M. Cacciari},

refereed = {yes},

length = {7},

url = {https://doi.org/10.22323/1.375.0013 }

}

[Schneider]

### A refined machinery to calculate large moments from coupled systems of linear differential equations

#### Johannes Blümlein, Peter Marquard, Carsten Schneider

In: 14th International Symposium on Radiative Corrections (RADCOR2019), D. Kosower, M. Cacciari (ed.), POS(RADCOR2019)078 , pp. 1-13. 2020. ISSN 1824-8039. arXiv:1912.04390 [cs.SC]. [url]@

author = {Johannes Blümlein and Peter Marquard and Carsten Schneider},

title = {{A refined machinery to calculate large moments from coupled systems of linear differential equations}},

booktitle = {{14th International Symposium on Radiative Corrections (RADCOR2019)}},

language = {english},

series = {POS(RADCOR2019)078},

pages = {1--13},

isbn_issn = {ISSN 1824-8039},

year = {2020},

note = {arXiv:1912.04390 [cs.SC]},

editor = {D. Kosower and M. Cacciari},

refereed = {yes},

length = {13},

url = {https://doi.org/10.22323/1.375.0078}

}

**inproceedings**{RISC6015,author = {Johannes Blümlein and Peter Marquard and Carsten Schneider},

title = {{A refined machinery to calculate large moments from coupled systems of linear differential equations}},

booktitle = {{14th International Symposium on Radiative Corrections (RADCOR2019)}},

language = {english},

series = {POS(RADCOR2019)078},

pages = {1--13},

isbn_issn = {ISSN 1824-8039},

year = {2020},

note = {arXiv:1912.04390 [cs.SC]},

editor = {D. Kosower and M. Cacciari},

refereed = {yes},

length = {13},

url = {https://doi.org/10.22323/1.375.0078}

}

[Schneider]

### The Polarized Three-Loop Anomalous Dimensions from a Massive Calculation

#### A. Behring, J. Blümlein, A. De Freitas, A. Goedicke, S. Klein, A. van Manteuffel, C. Schneider, K. Schönwald

In: 14th International Symposium on Radiative Corrections (RADCOR2019), D. Kosower, M. Cacciari (ed.), POS(RADCOR2019)047 arXiv:1911.06189 [hep-ph], pp. 1-10. 2020. ISSN 1824-8039. [url]@

author = {A. Behring and J. Blümlein and A. De Freitas and A. Goedicke and S. Klein and A. van Manteuffel and C. Schneider and K. Schönwald},

title = {{The Polarized Three-Loop Anomalous Dimensions from a Massive Calculation}},

booktitle = {{14th International Symposium on Radiative Corrections (RADCOR2019)}},

language = {english},

series = {POS(RADCOR2019)047},

number = {arXiv:1911.06189 [hep-ph]},

pages = {1--10},

isbn_issn = {ISSN 1824-8039},

year = {2020},

editor = {D. Kosower and M. Cacciari},

refereed = {yes},

length = {10},

url = {https://doi.org/10.22323/1.375.0047}

}

**inproceedings**{RISC6016,author = {A. Behring and J. Blümlein and A. De Freitas and A. Goedicke and S. Klein and A. van Manteuffel and C. Schneider and K. Schönwald},

title = {{The Polarized Three-Loop Anomalous Dimensions from a Massive Calculation}},

booktitle = {{14th International Symposium on Radiative Corrections (RADCOR2019)}},

language = {english},

series = {POS(RADCOR2019)047},

number = {arXiv:1911.06189 [hep-ph]},

pages = {1--10},

isbn_issn = {ISSN 1824-8039},

year = {2020},

editor = {D. Kosower and M. Cacciari},

refereed = {yes},

length = {10},

url = {https://doi.org/10.22323/1.375.0047}

}

[Schneider]

### The three-loop polarized pure singlet operator matrix element with two different masses

#### J. Ablinger, J. Blümlein, A. De Freitas, M. Saragnese, C. Schneider, K. Schönwald

Nuclear Physics B 952(114916), pp. 1-18. 2020. ISSN 0550-3213. arXiv:1911.11630 [hep-ph]. [url]@

author = {J. Ablinger and J. Blümlein and A. De Freitas and M. Saragnese and C. Schneider and K. Schönwald},

title = {{The three-loop polarized pure singlet operator matrix element with two different masses}},

language = {english},

journal = {Nuclear Physics B },

volume = {952},

number = {114916},

pages = {1--18},

isbn_issn = {ISSN 0550-3213},

year = {2020},

note = {arXiv:1911.11630 [hep-ph]},

refereed = {yes},

length = {18},

url = {https://doi.org/10.1016/j.nuclphysb.2020.114916}

}

**article**{RISC6017,author = {J. Ablinger and J. Blümlein and A. De Freitas and M. Saragnese and C. Schneider and K. Schönwald},

title = {{The three-loop polarized pure singlet operator matrix element with two different masses}},

language = {english},

journal = {Nuclear Physics B },

volume = {952},

number = {114916},

pages = {1--18},

isbn_issn = {ISSN 0550-3213},

year = {2020},

note = {arXiv:1911.11630 [hep-ph]},

refereed = {yes},

length = {18},

url = {https://doi.org/10.1016/j.nuclphysb.2020.114916}

}

[Schneider]

### Three loop heavy quark form factors and their asymptotic behavior

#### J. Ablinger, J. Blümlein, P. Marquard, N. Rana, C. Schneider

In: To appear in Proc.of 23rd DAE-BRNS High Energy Physics Symposium 2018, , pp. ?-?. 2020. arXiv:1906.05829 [hep-ph]. [url]@

author = {J. Ablinger and J. Blümlein and P. Marquard and N. Rana and C. Schneider},

title = {{Three loop heavy quark form factors and their asymptotic behavior}},

booktitle = {{To appear in Proc.of 23rd DAE-BRNS High Energy Physics Symposium 2018}},

language = {english},

pages = {?--?},

isbn_issn = {?},

year = {2020},

note = {arXiv:1906.05829 [hep-ph]},

editor = {?},

refereed = {no},

length = {8},

url = {https://arxiv.org/abs/1906.05829}

}

**inproceedings**{RISC6024,author = {J. Ablinger and J. Blümlein and P. Marquard and N. Rana and C. Schneider},

title = {{Three loop heavy quark form factors and their asymptotic behavior}},

booktitle = {{To appear in Proc.of 23rd DAE-BRNS High Energy Physics Symposium 2018}},

language = {english},

pages = {?--?},

isbn_issn = {?},

year = {2020},

note = {arXiv:1906.05829 [hep-ph]},

editor = {?},

refereed = {no},

length = {8},

url = {https://arxiv.org/abs/1906.05829}

}

[Schneider]

### The three-loop single mass polarized pure singlet operator matrix element

#### J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider, K. Schönwald

Nuclear Physics B 953(114945), pp. 1-25. 2020. ISSN 0550-3213. arXiv:1912.02536 [hep-ph]. [url]@

author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schönwald},

title = {{The three-loop single mass polarized pure singlet operator matrix element}},

language = {english},

journal = {Nuclear Physics B},

volume = {953},

number = {114945},

pages = {1--25},

isbn_issn = {ISSN 0550-3213},

year = {2020},

note = {arXiv:1912.02536 [hep-ph]},

refereed = {yes},

length = {25},

url = {https://doi.org/10.1016/j.nuclphysb.2020.114945}

}

**article**{RISC6075,author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schönwald},

title = {{The three-loop single mass polarized pure singlet operator matrix element}},

language = {english},

journal = {Nuclear Physics B},

volume = {953},

number = {114945},

pages = {1--25},

isbn_issn = {ISSN 0550-3213},

year = {2020},

note = {arXiv:1912.02536 [hep-ph]},

refereed = {yes},

length = {25},

url = {https://doi.org/10.1016/j.nuclphysb.2020.114945}

}

[Schneider]

### The Absent-Minded Passengers Problem: A Motivating Challenge Solved by Computer Algebra

#### C. Schneider

arXiv. Technical report, 2020. arXiv:2003.01921 [math.CO]. [url]@

author = {C. Schneider},

title = {{The Absent-Minded Passengers Problem: A Motivating Challenge Solved by Computer Algebra}},

language = {english},

year = {2020},

note = {arXiv:2003.01921 [math.CO]},

institution = {arXiv},

length = {11},

url = {https://arxiv.org/abs/2003.01921}

}

**techreport**{RISC6083,author = {C. Schneider},

title = {{The Absent-Minded Passengers Problem: A Motivating Challenge Solved by Computer Algebra}},

language = {english},

year = {2020},

note = {arXiv:2003.01921 [math.CO]},

institution = {arXiv},

length = {11},

url = {https://arxiv.org/abs/2003.01921}

}

[Schreiner]

### The Simulation of Finite-Source Retrial Queueing Systems with Collisions and Blocking

#### Ádam Tóth, Tamas Bérczes, Janos Sztrik, Attila Kuki, Wolfgang Schreiner

Journal of Mathematical Sciences 246(4), pp. 548-559. March 2020. ISSN 1573-8795. [url]@

author = {Ádam Tóth and Tamas Bérczes and Janos Sztrik and Attila Kuki and Wolfgang Schreiner},

title = {{The Simulation of Finite-Source Retrial Queueing Systems with Collisions and Blocking}},

language = {english},

abstract = {This paper investigates, using a simulation program, a retrial queuing system with a single server which is subject to random breakdowns. The number of sources of calls is finite, and collisions can take place. We assume that the failure of the server blocks the system’s operation such that newly arriving customers cannot enter the system, contrary to an earlier paper where the failure does not affect the arrivals. All the random variables included in the model construction are assumed to be independent of each other, and all times are exponentially distributed except for the service time, which is gamma distributed. The novelty of this analysis is the inspection of the blocking effect on the performance measures using different distributions. Various figures represent the impact of the squared coefficient of the variation of the service time on the main performance measures such as the mean and variance of the number of customers in the system, the mean and variance of the response time, the mean and variance of the time a customer spends in the service, and the mean and variance of the sojourn time in the orbit.},

journal = {Journal of Mathematical Sciences },

volume = {246},

number = {4},

pages = {548--559},

isbn_issn = {ISSN 1573-8795},

year = {2020},

month = {March},

refereed = {yes},

sponsor = {Austrian-Hungarian Bilateral Cooperation in Science and Tech- nology project 2017-2.2.4-TeT-AT-2017-00010},

length = {12},

url = {https://doi.org/10.1007/s10958-020-04759-4}

}

**article**{RISC6088,author = {Ádam Tóth and Tamas Bérczes and Janos Sztrik and Attila Kuki and Wolfgang Schreiner},

title = {{The Simulation of Finite-Source Retrial Queueing Systems with Collisions and Blocking}},

language = {english},

abstract = {This paper investigates, using a simulation program, a retrial queuing system with a single server which is subject to random breakdowns. The number of sources of calls is finite, and collisions can take place. We assume that the failure of the server blocks the system’s operation such that newly arriving customers cannot enter the system, contrary to an earlier paper where the failure does not affect the arrivals. All the random variables included in the model construction are assumed to be independent of each other, and all times are exponentially distributed except for the service time, which is gamma distributed. The novelty of this analysis is the inspection of the blocking effect on the performance measures using different distributions. Various figures represent the impact of the squared coefficient of the variation of the service time on the main performance measures such as the mean and variance of the number of customers in the system, the mean and variance of the response time, the mean and variance of the time a customer spends in the service, and the mean and variance of the sojourn time in the orbit.},

journal = {Journal of Mathematical Sciences },

volume = {246},

number = {4},

pages = {548--559},

isbn_issn = {ISSN 1573-8795},

year = {2020},

month = {March},

refereed = {yes},

sponsor = {Austrian-Hungarian Bilateral Cooperation in Science and Tech- nology project 2017-2.2.4-TeT-AT-2017-00010},

length = {12},

url = {https://doi.org/10.1007/s10958-020-04759-4}

}