Related papers: Polynomial Identities Implying Capparelli's Partit…

We provide a topological characterization of quivers whose path algebra satisfies a polynomial identity. This class includes the oriented cycle and acyclic quivers and, in the latter case, we describe the associated T-ideal. We introduce a…

We extend the methods and results of [arXiv 1603.04896] to the setting of multinomial distributions satisfying certain properties. These include all the multinomial distributions arising from the direct proof of the Central Limit Theorem…

Stanley introduces polynomials which help evaluate symmetric group characters and conjectures that the coefficients of the polynomials are positive. Stanley later gives a conjectured combinatorial interpretation for the coefficients of the…

Based on a bijection due to Fu and Tang, we provide combinatorial proofs of several partition identities of Andrews and Merca. We also introduce two weights for partitions to extend one of these identities.

This paper considers the properties of Tribonacci numbers on identities, matrices, and determinants. In the first front part, we obtain several symmetric identities of Tribonacci numbers by a matrix-based approach and binomial inversion…

The number of partitions of n into parts divisible by a or b equals the number of partitions of n in which each part and each difference of two parts is expressible as a non-negative integer combination of a or b. This generalizes…

Recently the second named author discovered a combinatorial identity in the context of vertex representations of quantum Kac-Moody algebras. We give a direct and elementary proof of this identity. Our method is to show a related identity of…

In previous work on Clebsch-Gordan coefficients, certain remarkable hexagonal arrays of integers are constructed that display behaviors found in Pascal's Triangle. We explain these behaviors further using the binomial transform and discrete…

In this paper, we give some new and interesting identities which are derived from the basis of Frobenius-Euler. Recently, Simsek et als(see [13]) have given some identities of q-analogue of Frobenius-Euler polynomials related to q-Bernstein…

We derive two new identities involving the Bernoulli numbers, the Euler numbers, and the Stirling numbers of the first kind using analytic continuation of a well known identity for the Stirling numbers of the first kind.

We prove analytic and combinatorial identities reminiscent of Schur's classical partition theorem. Specifically, we show that certain families of overpartitions whose parts satisfy gap conditions are equinumerous with partitions whose parts…

In this paper, we provide combinatorial proofs for certain partition identities which arise naturally in the context of Langlands' beyond endoscopy proposal. These partition identities motivate an explicit plethysm expansion of…

We use the method of tiling to give elementary combinatorial proofs of some celebrated $q$-series identities, such as Jacobi triple product identity, Rogers-Ramanujan identities, and some identities of Rogers. We give a tiling proof of the…

Recently, Andrews and Berkovich introduced a trinomial version of Bailey's lemma. In this note we show that each ordinary Bailey pair gives rise to a trinomial Bailey pair. This largely widens the applicability of the trinomial Bailey lemma…

We consider Tuenter polynomials as linear combinations of descending factorials and show that coefficients of these linear combinations are expressed via a Catalan triangle of numbers. We also describe a triangle of coefficients in terms of…

The two partition functions $p_\omega(n)$ and $p_\nu(n)$ were introduced by Andrews, Dixit and Yee, which are related to the third order mock theta functions $\omega(q)$ and $\nu(q)$, respectively. Recently, Andrews and Yee analytically…

This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem,…

We prove a theorem which add a new member to Rogers-Ramanujan identities. This new member counts partitions with different type of constraints on even and odd parts. Generalizing this theorem, we obtain two family of partition identities of…

In this paper, we present several new $q$-congruences on the $q$-trinomial coefficients introduced by Andrews and Baxter. As a conclusion, we obtain the following congruence: \begin{align*}…

Infinitely many Casoratian identities are derived for the Wilson and Askey-Wilson polynomials in parallel to the Wronskian identities for the Hermite, Laguerre and Jacobi polynomials, which were reported recently by the present authors.…