Computer Algebra and Combinatorial Inequalities [FWF SFB F050-07]
Project Lead
Project Duration
01/03/2013 - 31/07/2022Project URL
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Partners
The Austrian Science Fund (FWF)
Software
qFunctions
The qFunctions package is a Mathematica package for q-series and partition theory applications.
The qFunctions package by Jakob Ablinger and Ali K. Uncu is a Mathematica package for q-series and partition theory applications. This package includes both experimental and symbolic tools. The experimental set of elements includes guessers for q-shift equations and recurrences ...
Authors: Jakob Ablinger, Ali Uncu
MorePublications
2019
[Berkovich]
Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series Identities
Ali Kemal Uncu, Alexander Berkovich
ArXiv e-prints (accepted), pp. 1-10. 2019. N/A. [url]@article{RISC5801,
author = {Ali Kemal Uncu and Alexander Berkovich},
title = {{Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series Identities }},
language = {english},
abstract = {We will prove an identity involving refined q-trinomial coefficients. We then extend this identity to two infinite families of doubly bounded polynomial identities using transformation properties of the refined q-trinomials in an iterative fashion in the spirit of Bailey chains. One of these two hierarchies contains an identity which is equivalent to Capparelli's first Partition Theorem. },
journal = {ArXiv e-prints (accepted)},
pages = {1--10},
isbn_issn = {N/A},
year = {2019},
refereed = {yes},
length = {10},
url = {https://arxiv.org/abs/1810.12048}
}
author = {Ali Kemal Uncu and Alexander Berkovich},
title = {{Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series Identities }},
language = {english},
abstract = {We will prove an identity involving refined q-trinomial coefficients. We then extend this identity to two infinite families of doubly bounded polynomial identities using transformation properties of the refined q-trinomials in an iterative fashion in the spirit of Bailey chains. One of these two hierarchies contains an identity which is equivalent to Capparelli's first Partition Theorem. },
journal = {ArXiv e-prints (accepted)},
pages = {1--10},
isbn_issn = {N/A},
year = {2019},
refereed = {yes},
length = {10},
url = {https://arxiv.org/abs/1810.12048}
}
[Jimenez Pastor]
A Computable Extension for Holonomic Functions: DD-Finite Functions
Jiménez-Pastor Antonio, Pillwein Veronika
Journal of Symbolic Computation 94, pp. 90-104. September-October 2019. ISSN 0747-7171. [doi]@article{RISC5831,
author = {Jiménez-Pastor Antonio and Pillwein Veronika},
title = {{A Computable Extension for Holonomic Functions: DD-Finite Functions}},
language = {english},
abstract = {Differentiably finite (D-finite) formal power series form a large class of useful functions for which a variety of symbolic algorithms exists. Among these methods are several closure properties that can be carried out automatically. We introduce a natural extension of these functions to a larger class of computable objects for which we prove closure properties. These are again algorithmic. This extension can be iterated constructively preserving the closure properties},
journal = {Journal of Symbolic Computation},
volume = {94},
pages = {90--104},
isbn_issn = {ISSN 0747-7171},
year = {2019},
month = {September-October},
refereed = {yes},
length = {15},
url = {https://doi.org/10.1016/j.jsc.2018.07.002}
}
author = {Jiménez-Pastor Antonio and Pillwein Veronika},
title = {{A Computable Extension for Holonomic Functions: DD-Finite Functions}},
language = {english},
abstract = {Differentiably finite (D-finite) formal power series form a large class of useful functions for which a variety of symbolic algorithms exists. Among these methods are several closure properties that can be carried out automatically. We introduce a natural extension of these functions to a larger class of computable objects for which we prove closure properties. These are again algorithmic. This extension can be iterated constructively preserving the closure properties},
journal = {Journal of Symbolic Computation},
volume = {94},
pages = {90--104},
isbn_issn = {ISSN 0747-7171},
year = {2019},
month = {September-October},
refereed = {yes},
length = {15},
url = {https://doi.org/10.1016/j.jsc.2018.07.002}
}
[Pillwein]
On the positivity of the Gillis–Reznick–Zeilberger rational function
V. Pillwein
Advances in Applied Mathematics 104, pp. 75 - 84. 2019. ISSN 0196-8858. [url]@article{RISC5813,
author = {V. Pillwein},
title = {{On the positivity of the Gillis–Reznick–Zeilberger rational function}},
language = {english},
journal = {Advances in Applied Mathematics},
volume = {104},
pages = {75 -- 84},
isbn_issn = { ISSN 0196-8858},
year = {2019},
refereed = {yes},
keywords = {Positivity, Cylindrical decomposition, Rational function, Symbolic summation},
length = {10},
url = {http://www.sciencedirect.com/science/article/pii/S0196885818301179}
}
author = {V. Pillwein},
title = {{On the positivity of the Gillis–Reznick–Zeilberger rational function}},
language = {english},
journal = {Advances in Applied Mathematics},
volume = {104},
pages = {75 -- 84},
isbn_issn = { ISSN 0196-8858},
year = {2019},
refereed = {yes},
keywords = {Positivity, Cylindrical decomposition, Rational function, Symbolic summation},
length = {10},
url = {http://www.sciencedirect.com/science/article/pii/S0196885818301179}
}
[Uncu]
A Polynomial Identity Implying Schur's Partition Theorem
Ali Kemal Uncu
ArXiv e-prints (submitted), pp. 1-11. 2019. N/A. [url]@article{RISC5898,
author = {Ali Kemal Uncu},
title = {{A Polynomial Identity Implying Schur's Partition Theorem }},
language = {english},
abstract = {We propose and prove a new polynomial identity that implies Schur's partition theorem. We give combinatorial interpretations of some of our expressions in the spirit of Kurşungöz. We also present some related polynomial and q-series identities. },
journal = {ArXiv e-prints (submitted)},
pages = {1--11},
isbn_issn = {N/A},
year = {2019},
refereed = {yes},
length = {11},
url = {https://arxiv.org/abs/1903.01157}
}
author = {Ali Kemal Uncu},
title = {{A Polynomial Identity Implying Schur's Partition Theorem }},
language = {english},
abstract = {We propose and prove a new polynomial identity that implies Schur's partition theorem. We give combinatorial interpretations of some of our expressions in the spirit of Kurşungöz. We also present some related polynomial and q-series identities. },
journal = {ArXiv e-prints (submitted)},
pages = {1--11},
isbn_issn = {N/A},
year = {2019},
refereed = {yes},
length = {11},
url = {https://arxiv.org/abs/1903.01157}
}
2018
[Berkovich]
On some polynomials and series of Bloch-Polya Type
Berkovich A., Uncu A. K.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 146(7), pp. 2827-2838. July 2018. 1088-6826. [url]@article{RISC5557,
author = {Berkovich A. and Uncu A.~K.},
title = {{On some polynomials and series of Bloch-Polya Type}},
language = {english},
journal = {PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY},
volume = {146},
number = {7},
pages = {2827--2838},
isbn_issn = {1088-6826},
year = {2018},
month = {July},
refereed = {yes},
keywords = {Mathematics - Number Theory, Mathematics - Combinatorics, 05A17, 05A19, 11B65, 11P81},
length = {12},
url = {http://www.ams.org/journals/proc/2018-146-07/S0002-9939-2018-13982-9/}
}
author = {Berkovich A. and Uncu A.~K.},
title = {{On some polynomials and series of Bloch-Polya Type}},
language = {english},
journal = {PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY},
volume = {146},
number = {7},
pages = {2827--2838},
isbn_issn = {1088-6826},
year = {2018},
month = {July},
refereed = {yes},
keywords = {Mathematics - Number Theory, Mathematics - Combinatorics, 05A17, 05A19, 11B65, 11P81},
length = {12},
url = {http://www.ams.org/journals/proc/2018-146-07/S0002-9939-2018-13982-9/}
}
[Berkovich]
Some Elementary Partition Inequalities and Their Implications
Berkovich A., Uncu A. K.
ArXiv e-prints (to appear in Annals of Cobinatorics), pp. -. 2018. Preprint. [url]@article{RISC5558,
author = {Berkovich A. and Uncu A.~K.},
title = {{Some Elementary Partition Inequalities and Their Implications}},
language = {english},
journal = {ArXiv e-prints (to appear in Annals of Cobinatorics)},
pages = {--},
isbn_issn = {Preprint},
year = {2018},
refereed = {yes},
keywords = {Mathematics - Combinatorics, Mathematics - Number Theory, 05A15, 05A17, 05A19, 05A20, 11B65, 11P81, 11P84, 33D15},
length = {12},
url = {https://arxiv.org/abs/1708.01957}
}
author = {Berkovich A. and Uncu A.~K.},
title = {{Some Elementary Partition Inequalities and Their Implications}},
language = {english},
journal = {ArXiv e-prints (to appear in Annals of Cobinatorics)},
pages = {--},
isbn_issn = {Preprint},
year = {2018},
refereed = {yes},
keywords = {Mathematics - Combinatorics, Mathematics - Number Theory, 05A15, 05A17, 05A19, 05A20, 11B65, 11P81, 11P84, 33D15},
length = {12},
url = {https://arxiv.org/abs/1708.01957}
}
[Jimenez Pastor]
Algorithmic Arithmetics with DD-Finite Functions
Jiménez-Pastor Antonio, Pillwein Veronika
In: Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation, Arreche Carlos (ed.), ISSAC '18 , pp. 231-237. 2018. ACM, New York, NY, USA, ISBN 978-1-4503-5550-6. [doi]@inproceedings{RISC5730,
author = {Jiménez-Pastor Antonio and Pillwein Veronika},
title = {{Algorithmic Arithmetics with DD-Finite Functions}},
booktitle = {{Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation}},
language = {english},
series = {ISSAC '18},
pages = {231--237},
publisher = {ACM},
address = {New York, NY, USA},
isbn_issn = {ISBN 978-1-4503-5550-6},
year = {2018},
editor = {Arreche Carlos},
refereed = {yes},
keywords = {algorithms, closure properties, holonomic functions},
length = {7},
url = {http://doi.acm.org/10.1145/3208976.3209009}
}
author = {Jiménez-Pastor Antonio and Pillwein Veronika},
title = {{Algorithmic Arithmetics with DD-Finite Functions}},
booktitle = {{Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation}},
language = {english},
series = {ISSAC '18},
pages = {231--237},
publisher = {ACM},
address = {New York, NY, USA},
isbn_issn = {ISBN 978-1-4503-5550-6},
year = {2018},
editor = {Arreche Carlos},
refereed = {yes},
keywords = {algorithms, closure properties, holonomic functions},
length = {7},
url = {http://doi.acm.org/10.1145/3208976.3209009}
}
[Pillwein]
Positivity of the Gillis-Reznick-Zeilberger rational function
V. Pillwein
Technical report no. 18-05 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). 2018. [pdf]@techreport{RISC5612,
author = {V. Pillwein},
title = {{Positivity of the Gillis-Reznick-Zeilberger rational function}},
language = {english},
number = {18-05},
year = {2018},
length = {12},
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)}
}
author = {V. Pillwein},
title = {{Positivity of the Gillis-Reznick-Zeilberger rational function}},
language = {english},
number = {18-05},
year = {2018},
length = {12},
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)}
}
2017
[Berkovich]
Variation on a theme of Nathan Fine. New weighted partition identities
Berkovich Alexander, Uncu Ali K.
J. Number Theory 176, pp. 226-248. 2017. ISSN 0022-314X. [doi]@article{RISC5552,
author = {Berkovich Alexander and Uncu Ali K.},
title = {{Variation on a theme of Nathan Fine. New weighted partition identities}},
language = {english},
journal = {J. Number Theory},
volume = {176},
pages = {226--248},
isbn_issn = { ISSN 0022-314X},
year = {2017},
refereed = {yes},
length = {23},
url = {https://doi.org/10.1016/j.jnt.2016.12.011}
}
author = {Berkovich Alexander and Uncu Ali K.},
title = {{Variation on a theme of Nathan Fine. New weighted partition identities}},
language = {english},
journal = {J. Number Theory},
volume = {176},
pages = {226--248},
isbn_issn = { ISSN 0022-314X},
year = {2017},
refereed = {yes},
length = {23},
url = {https://doi.org/10.1016/j.jnt.2016.12.011}
}
[Uncu]
Weighted Rogers-Ramanujan partitions and Dyson crank
Uncu Ali Kemal
The Ramanujan Journal, pp. -. May 2017. ISSN 1572-9303. [doi]@article{RISC5555,
author = {Uncu Ali Kemal},
title = {{Weighted Rogers--Ramanujan partitions and Dyson crank}},
language = {english},
abstract = {In this paper, we refine a weighted partition identity of Alladi. We write formulas for generating functions for the number of partitions grouped with respect to a partition statistic other than the norm. We tie our weighted results as well as the different statistics with the crank of a partition. In particular, we prove that the number of partitions into even number of distinct parts whose odd-indexed parts' sum is n is equal to the number of partitions of n with non-negative crank.},
journal = {The Ramanujan Journal},
pages = {--},
isbn_issn = { ISSN 1572-9303},
year = {2017},
month = {May},
refereed = {yes},
length = {0},
url = {https://doi.org/10.1007/s11139-017-9903-8}
}
author = {Uncu Ali Kemal},
title = {{Weighted Rogers--Ramanujan partitions and Dyson crank}},
language = {english},
abstract = {In this paper, we refine a weighted partition identity of Alladi. We write formulas for generating functions for the number of partitions grouped with respect to a partition statistic other than the norm. We tie our weighted results as well as the different statistics with the crank of a partition. In particular, we prove that the number of partitions into even number of distinct parts whose odd-indexed parts' sum is n is equal to the number of partitions of n with non-negative crank.},
journal = {The Ramanujan Journal},
pages = {--},
isbn_issn = { ISSN 1572-9303},
year = {2017},
month = {May},
refereed = {yes},
length = {0},
url = {https://doi.org/10.1007/s11139-017-9903-8}
}
2016
[Berkovich]
On partitions with fixed number of even-indexed and odd-indexed odd parts
Berkovich Alexander, Uncu Ali Kemal
J. Number Theory 167, pp. 7-30. 2016. ISSN 0022-314X. [doi]@article{RISC5553,
author = {Berkovich Alexander and Uncu Ali Kemal},
title = {{On partitions with fixed number of even-indexed and odd-indexed odd parts}},
language = {english},
journal = {J. Number Theory},
volume = {167},
pages = {7--30},
isbn_issn = { ISSN 0022-314X},
year = {2016},
refereed = {yes},
length = {24},
url = {https://doi.org/10.1016/j.jnt.2016.02.031}
}
author = {Berkovich Alexander and Uncu Ali Kemal},
title = {{On partitions with fixed number of even-indexed and odd-indexed odd parts}},
language = {english},
journal = {J. Number Theory},
volume = {167},
pages = {7--30},
isbn_issn = { ISSN 0022-314X},
year = {2016},
refereed = {yes},
length = {24},
url = {https://doi.org/10.1016/j.jnt.2016.02.031}
}
[Berkovich]
New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions
Berkovich A., Kemal Uncu A.
ALLADI60 2016: Analytic Number Theory, Modular Forms and q-Hypergeometric Series , pp. -. 2016. 978-3-319-68375-1. [url]@article{RISC5556,
author = {Berkovich A. and Kemal Uncu A.},
title = {{New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions}},
language = {english},
journal = {ALLADI60 2016: Analytic Number Theory, Modular Forms and q-Hypergeometric Series },
pages = {--},
isbn_issn = {978-3-319-68375-1},
year = {2016},
refereed = {yes},
keywords = {Mathematics - Number Theory, Mathematics - Combinatorics, 05A15, 05A17, 05A19, 11B34, 11B75, 11P81, 11P84, 33D15},
length = {0},
url = {https://link.springer.com/book/10.1007/978-3-319-68376-8}
}
author = {Berkovich A. and Kemal Uncu A.},
title = {{New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions}},
language = {english},
journal = {ALLADI60 2016: Analytic Number Theory, Modular Forms and q-Hypergeometric Series },
pages = {--},
isbn_issn = {978-3-319-68375-1},
year = {2016},
refereed = {yes},
keywords = {Mathematics - Number Theory, Mathematics - Combinatorics, 05A15, 05A17, 05A19, 11B34, 11B75, 11P81, 11P84, 33D15},
length = {0},
url = {https://link.springer.com/book/10.1007/978-3-319-68376-8}
}
[Paule]
A new witness identity for $11|p(11n+6)$
Peter Paule, Cristian-Silviu Radu
In: Analytic Number Theory, Modular Forms and q-Hypergeometric Series, George E. Andrews, Frank Garvan (ed.), pp. 625-640. 2016. Springer, 2194-1009. [pdf]@inproceedings{RISC5329,
author = {Peter Paule and Cristian-Silviu Radu},
title = {{A new witness identity for $11|p(11n+6)$}},
booktitle = {{Analytic Number Theory, Modular Forms and q-Hypergeometric Series}},
language = {english},
pages = {625--640},
publisher = {Springer},
isbn_issn = { 2194-1009},
year = {2016},
editor = { George E. Andrews and Frank Garvan},
refereed = {yes},
length = {16}
}
author = {Peter Paule and Cristian-Silviu Radu},
title = {{A new witness identity for $11|p(11n+6)$}},
booktitle = {{Analytic Number Theory, Modular Forms and q-Hypergeometric Series}},
language = {english},
pages = {625--640},
publisher = {Springer},
isbn_issn = { 2194-1009},
year = {2016},
editor = { George E. Andrews and Frank Garvan},
refereed = {yes},
length = {16}
}
2015
[Berkovich]
A new companion to Capparelli's identities
Berkovich Alexander, Uncu Ali Kemal
Adv. in Appl. Math. 71, pp. 125-137. 2015. ISSN 0196-8858. [doi]@article{RISC5554,
author = {Berkovich Alexander and Uncu Ali Kemal},
title = {{A new companion to Capparelli's identities}},
language = {english},
journal = {Adv. in Appl. Math.},
volume = {71},
pages = {125--137},
isbn_issn = { ISSN 0196-8858},
year = {2015},
refereed = {yes},
length = {13},
url = {https://doi.org/10.1016/j.aam.2015.09.012}
}
author = {Berkovich Alexander and Uncu Ali Kemal},
title = {{A new companion to Capparelli's identities}},
language = {english},
journal = {Adv. in Appl. Math.},
volume = {71},
pages = {125--137},
isbn_issn = { ISSN 0196-8858},
year = {2015},
refereed = {yes},
length = {13},
url = {https://doi.org/10.1016/j.aam.2015.09.012}
}
[Pillwein]
Proof of a conjecture of M. Patrick concerning Jacobi polynomials
A. Alexandrov, H. Dietert, G. Nikolov, V. Pillwein
Journal of Mathematical Analysis and Applications 428(2), pp. 750-761. 2015.@article{RISC5140,
author = {A. Alexandrov and H. Dietert and G. Nikolov and V. Pillwein},
title = {{Proof of a conjecture of M. Patrick concerning Jacobi polynomials }},
language = {english},
journal = {Journal of Mathematical Analysis and Applications},
volume = {428},
number = {2},
pages = {750--761},
isbn_issn = {?},
year = {2015},
refereed = {yes},
length = {12}
}
author = {A. Alexandrov and H. Dietert and G. Nikolov and V. Pillwein},
title = {{Proof of a conjecture of M. Patrick concerning Jacobi polynomials }},
language = {english},
journal = {Journal of Mathematical Analysis and Applications},
volume = {428},
number = {2},
pages = {750--761},
isbn_issn = {?},
year = {2015},
refereed = {yes},
length = {12}
}
[Pillwein]
Symbolic Computation and Finite Element Methods.
V. Pillwein
In: CASC 2015, V.P. Gerdt, W. Koepf, W.M. Seiler, and E.V. Vorozhtsov (ed.), LNCS 9301, pp. 374-388. 2015. Springer-Verlag Berlin Heidelberg, 0302-9743. [pdf]@inproceedings{RISC5182,
author = {V. Pillwein},
title = {{Symbolic Computation and Finite Element Methods.}},
booktitle = {{CASC 2015}},
language = {english},
series = {LNCS},
volume = {9301},
pages = {374--388},
publisher = {Springer-Verlag Berlin Heidelberg},
isbn_issn = {0302-9743},
year = {2015},
editor = {V.P. Gerdt and W. Koepf and W.M. Seiler and and E.V. Vorozhtsov},
refereed = {no},
length = {15}
}
author = {V. Pillwein},
title = {{Symbolic Computation and Finite Element Methods.}},
booktitle = {{CASC 2015}},
language = {english},
series = {LNCS},
volume = {9301},
pages = {374--388},
publisher = {Springer-Verlag Berlin Heidelberg},
isbn_issn = {0302-9743},
year = {2015},
editor = {V.P. Gerdt and W. Koepf and W.M. Seiler and and E.V. Vorozhtsov},
refereed = {no},
length = {15}
}
[Schussler]
An efficient procedure deciding positivity for a class of holonomic sequences
V. Pillwein, M. Schussler
ACM Communications in Computer Algebra 49(3), pp. 90-93. 2015. Extended abstract of the poster presentation at ISSAC 2015. [pdf]@article{RISC5617,
author = {V. Pillwein and M. Schussler},
title = {{An efficient procedure deciding positivity for a class of holonomic sequences}},
language = {english},
journal = {ACM Communications in Computer Algebra},
volume = {49},
number = {3},
pages = {90--93},
isbn_issn = { },
year = {2015},
note = {Extended abstract of the poster presentation at ISSAC 2015},
refereed = {yes},
length = {4}
}
author = {V. Pillwein and M. Schussler},
title = {{An efficient procedure deciding positivity for a class of holonomic sequences}},
language = {english},
journal = {ACM Communications in Computer Algebra},
volume = {49},
number = {3},
pages = {90--93},
isbn_issn = { },
year = {2015},
note = {Extended abstract of the poster presentation at ISSAC 2015},
refereed = {yes},
length = {4}
}
2012
[Zafeirakopoulos]
Linear Diophantine Systems: Partition Analysis and Polyhedral Geometry
Zafeirakis Zafeirakopoulos
Research Institute for Symbolic Computation / DK-compmath. PhD Thesis. December 2012. [pdf]@phdthesis{RISC4715,
author = {Zafeirakis Zafeirakopoulos},
title = {{Linear Diophantine Systems: Partition Analysis and Polyhedral Geometry}},
language = {english},
year = {2012},
month = {December},
translation = {0},
school = {Research Institute for Symbolic Computation / DK-compmath},
length = {0}
}
author = {Zafeirakis Zafeirakopoulos},
title = {{Linear Diophantine Systems: Partition Analysis and Polyhedral Geometry}},
language = {english},
year = {2012},
month = {December},
translation = {0},
school = {Research Institute for Symbolic Computation / DK-compmath},
length = {0}
}
