Dr. Ali Uncu

Research Area

Integer Partitions, q-Series, Combinatorics

My personal website: www.akuncu.com.

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

2021

[Uncu]

qFunctions - A Mathematica package for q-series and partition theory applications

J. Ablinger, A. Uncu

Journal of Symbolic Computation 107, pp. 145-166. 2021. ISSN 0747-7171. arXiv:1910.12410. [doi]

[bib]

@article{RISC6299,
author = {J. Ablinger and A. Uncu},
title = {{qFunctions -- A Mathematica package for q-series and partition theory applications}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {107},
pages = {145--166},
isbn_issn = {ISSN 0747-7171},
year = {2021},
note = {arXiv:1910.12410},
refereed = {yes},
length = {22},
url = {https://doi.org/10.1016/j.jsc.2021.02.003}
}

2019

[Uncu]

Polynomial Identities Implying Capparelli's Partition Theorems

Ali Kemal Uncu, Alexander Berkovich

Accepted - Journal of Number Theory, pp. -. 2019. N/A. [url]

[bib]

@article{RISC5790,
author = {Ali Kemal Uncu and Alexander Berkovich},
title = {{Polynomial Identities Implying Capparelli's Partition Theorems }},
language = {english},
journal = {Accepted - Journal of Number Theory},
pages = {--},
isbn_issn = {N/A},
year = {2019},
refereed = {yes},
length = {21},
url = {https://arxiv.org/pdf/1807.10974.pdf}
}

[Uncu]

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]

[bib]

@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}
}

[Uncu]

A Polynomial Identity Implying Schur's Partition Theorem

Ali Kemal Uncu

ArXiv e-prints (submitted), pp. 1-11. 2019. N/A. [url]

[bib]

@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}
}

2018

[Uncu]

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]

[bib]

@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/}
}

[Uncu]

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]

[bib]

@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}
}

[Uncu]

Elementary Polynomial Identities Involving q-Trinomial Coefficients

Ali Kemal Uncu, Alexander Berkovich

ArXiv e-prints (submitted), pp. -. 2018. N/A. [url]

[bib]

@article{RISC5791,
author = {Ali Kemal Uncu and Alexander Berkovich},
title = {{Elementary Polynomial Identities Involving q-Trinomial Coefficients }},
language = {english},
journal = {ArXiv e-prints (submitted)},
pages = {--},
isbn_issn = {N/A},
year = {2018},
refereed = {yes},
length = {0},
url = {https://arxiv.org/abs/1810.06497}
}

[Uncu]

On double sum generating functions in connection with some classical partition theorems

Ali Kemal Uncu

ArXiv e-prints, pp. 1-20. 2018. N/A.

[bib]

@article{RISC5800,
author = {Ali Kemal Uncu},
title = {{On double sum generating functions in connection with some classical partition theorems }},
language = {english},
abstract = { We focus on writing closed forms of generating functions for the number of partitions with gap conditions as double sums starting from a combinatorial construction. Some examples of the sets of partitions with gap conditions to be discussed here are the set of Rogers--Ramanujan, Göllnitz--Gordon, and little Göllnitz partitions. This work also includes finding the finite analogs of the related generating functions and the discussion of some related series and polynomial identities. Additionally, we present a different construction and a double sum representation for the products similar to the ones that appear in the Rogers--Ramanujan identities. },
journal = {ArXiv e-prints},
pages = {1--20},
isbn_issn = {N/A},
year = {2018},
refereed = {yes},
length = {20}
}

2017

[Uncu]

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]

[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}
}

[Uncu]

Weighted Rogers-Ramanujan partitions and Dyson crank

Uncu Ali Kemal

The Ramanujan Journal, pp. -. May 2017. ISSN 1572-9303. [doi]

[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

[Uncu]

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]

[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}
}

[Uncu]

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]

[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 = {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}
}

2015

[Uncu]

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]

[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}
}