Zobrazeno 1 - 10
of 59
pro vyhledávání: '"Uncu, Ali Kemal"'
Autor:
Mandlmayr, Michael, Uncu, Ali Kemal
We present effective procedures to calculate regular normal cones and other related objects using quantifier elimination. This method of normal cone calculations is complementary to computing Lagrangians and it works best at points where the constrai
Externí odkaz:
http://arxiv.org/abs/2402.05579
The Factorial Basis method, initially designed for quasi-triangular, shift-compatible factorial bases, provides solutions to linear recurrence equations in the form of definite-sums. This paper extends the Factorial Basis method to its q-analog, enab
Externí odkaz:
http://arxiv.org/abs/2402.04392
Autor:
Uncu, Ali Kemal
We present proofs of two new families of sum-product identities arising from the cylindric partitions paradigm. Most of the presented expressions, the related sum-product identities, and the ingredients for the proofs were first conjectured by Kanade
Externí odkaz:
http://arxiv.org/abs/2301.01359
Autor:
Berkovich, Alexander, Uncu, Ali Kemal
We refine Schmidt's problem and a partition identity related to 2-color partitions which we will refer to as Uncu-Andrews-Paule theorem. We will approach the problem using Boulet-Stanley weights and a formula on Rogers-Szeg\H{o} polynomials by Berkov
Externí odkaz:
http://arxiv.org/abs/2205.00527
Autor:
Berkovich, Alexander, Uncu, Ali Kemal
We prove a new polynomial refinement of the Capparelli's identities. Using a special case of Bailey's lemma we prove many infinite families of sum-product identities that root from our finite analogues of Capparelli's identities. We also discuss the
Externí odkaz:
http://arxiv.org/abs/2106.09773
Autor:
Ablinger, Jakob, Uncu, Ali Kemal
Publikováno v:
In Journal of Symbolic Computation November-December 2021 107:145-166
Autor:
Berkovich, Alexander, Uncu, Ali Kemal
We use the $q$-binomial theorem, the $q$-Gauss sum, and the ${}_2\phi_1 \rightarrow {}_2\phi_2$ transformation of Jackson to discover and prove many new weighted partition identities. These identities involve unrestricted partitions, overpartitions,
Externí odkaz:
http://arxiv.org/abs/1608.00193
Autor:
Berkovich, Alexander, Uncu, Ali Kemal
We utilize false theta function results of Nathan Fine to discover three new partition identities involving weights. These relations connect G\"ollnitz--Gordon type partitions and partitions with distinct odd parts, partitions into distinct parts and
Externí odkaz:
http://arxiv.org/abs/1605.00291
Autor:
Uncu, Ali Kemal
In this paper we refine a weighted partition identity of Alladi. We write explicit formulas of generating functions for the number of partitions grouped with respect to a partition statistic other than the norm. We tie our weighted results and the di
Externí odkaz:
http://arxiv.org/abs/1603.00399