Computer Algebra and Combinatorial Inequalities [F050-07]

Project Lead

Project Duration

01/03/2013 - 28/02/2021

Project URL

Project Website

Publications

2018

On some polynomials and series of Bloch-Polya Type

Berkovich A., Uncu A. K.

ArXiv e-prints (to appear in Proc. of AMS ), pp. -. 2018. Preprint.
[bib]
@article{RISC5557,
author = {Berkovich A. and Uncu A.~K.},
title = {{On some polynomials and series of Bloch-Polya Type}},
language = {english},
journal = {ArXiv e-prints (to appear in Proc. of AMS )},
pages = {--},
isbn_issn = {Preprint},
year = {2018},
refereed = {yes},
keywords = {Mathematics - Number Theory, Mathematics - Combinatorics, 05A17, 05A19, 11B65, 11P81},
length = {0}
}

Some Elementary Partition Inequalities and Their Implications

Berkovich A., Uncu A. K.

ArXiv e-prints (submitted), pp. -. 2018. Preprint.
[bib]
@article{RISC5558,
author = {Berkovich A. and Uncu A.~K.},
title = {{Some Elementary Partition Inequalities and Their Implications}},
language = {english},
journal = {ArXiv e-prints (submitted)},
pages = {--},
isbn_issn = {Preprint},
year = {2018},
refereed = {yes},
keywords = {Mathematics - Combinatorics, Mathematics - Number Theory, 05A15, 05A17, 05A19, 05A20, 11B65, 11P81, 11P84, 33D15},
length = {0}
}

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. [url]
[bib]
@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}
}

A Computable Extension for Holonomic Functions: DD-Finite Functions

Jiménez-Pastor Antonio, Pillwein Veronika

Journal of Symbolic Computation, pp. -. 2018. ISSN 0747-7171. accepted.
[bib]
@article{RISC5731,
author = {Jiménez-Pastor Antonio and Pillwein Veronika},
title = {{A Computable Extension for Holonomic Functions: DD-Finite Functions}},
language = {english},
journal = {Journal of Symbolic Computation},
pages = {--},
isbn_issn = {ISSN 0747-7171},
year = {2018},
note = {accepted},
refereed = {yes},
length = {0}
}

2017

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. [url]
[bib]
@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}
}

Weighted Rogers-Ramanujan partitions and Dyson crank

Uncu Ali Kemal

The Ramanujan Journal, pp. -. May 2017. ISSN 1572-9303. [url]
[bib]
@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}
}

2016

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. [url]
[bib]
@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}
}

New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions

Berkovich A., Kemal Uncu A.

ArXiv e-prints (to appear in Proc. of GNV 2016 Int. Conf. ), pp. -. 2016. Preprint.
[bib]
@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 = {ArXiv e-prints (to appear in Proc. of GNV 2016 Int. Conf. )},
pages = {--},
isbn_issn = {Preprint},
year = {2016},
refereed = {yes},
keywords = {Mathematics - Number Theory, Mathematics - Combinatorics, 05A15, 05A17, 05A19, 11B34, 11B75, 11P81, 11P84, 33D15},
length = {0}
}

A New Witness Identity for $11|p(11n+6)$

Peter Paule, Cristian-Silviu Radu

In: status submitted, , pp. -. 2016. [pdf]
[bib]
@inproceedings{RISC5329,
author = {Peter Paule and Cristian-Silviu Radu},
title = {{A New Witness Identity for $11|p(11n+6)$}},
booktitle = {{status submitted}},
language = {english},
pages = {--},
isbn_issn = { },
year = {2016},
editor = { },
refereed = {yes},
length = {11}
}

2015

A new companion to Capparelli's identities

Berkovich Alexander, Uncu Ali Kemal

Adv. in Appl. Math. 71, pp. 125-137. 2015. ISSN 0196-8858. [url]
[bib]
@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}
}

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.
[bib]
@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}
}

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]
[bib]
@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}
}

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]
[bib]
@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}
}

2012

Linear Diophantine Systems: Partition Analysis and Polyhedral Geometry

Zafeirakis Zafeirakopoulos

Research Institute for Symbolic Computation / DK-compmath. PhD Thesis. December 2012. [pdf]
[bib]
@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}
}

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