81 citations · 484 across the 73 of their papers we have counts for
59 papers · 1 filter
Real-rootedness of the type A minuscule polynomials
Ming-Jian Ding, Jiang Zeng
We prove two recent conjectures of Bourn and Erickson (2023) regarding the real-rootedness of a certain family of polynomials as well as the sum of their coefficients. The…
Proof of an explicit formula for a series from Ramanujan's Notebooks via tree functions
Ming-Jian Ding, Jiang Zeng
We prove a recent conjecture, due to Vigren and Dieckmann, about an explicit triple sum formula for a series from Ramanujan's Notebooks. We shall give two proofs: the first one is…
Some identities involving -Stirling numbers of the second kind in type B
Ming-Jian Ding, Jiang Zeng
The recent interest in -Stirling numbers of the second kind in type B prompted us to give a type B analogue of a classical identity connecting the -Stirling numbers of the se…
-Catalan numbers: gamma expansions, pattern avoidance and the -phenomenon
Shishuo Fu, Dazhao Tang, Bin Han +1
The aim of this paper is two-fold. We first prove several new interpretations of a kind of -Catalan numbers along with their corresponding -expansions using pattern avoid…
A -Clausen-Orr type formula and its applications
Hong-Fang Guo, Victor J. W. Guo, Jiang Zeng
We show that certain terminating series can be factorized into a product of two series. As applications we prove a summation formula for a product of two -…
A unifying combinatorial approach to refined little Göllnitz and Capparelli's companion identities
Shishuo Fu, Jiang Zeng
Berkovich-Uncu have recently proved a companion of the well-known Capparelli's identities as well as refinements of Savage-Sills' new little Göllnitz identities. Noticing the conne…
On two unimodal descent polynomials
Shishuo Fu, Zhicong Lin, Jiang Zeng
The descent polynomials of separable permutations and derangements are both demonstrated to be unimodal. Moreover, we prove that the -coefficients of the first are positive with…
Symmetric unimodal expansions of excedances in colored permutations
Heesung Shin, Jiang Zeng
We consider several generalizations of the classical -positivity of Eulerian polynomials (and their derangement analogues) using generating functions and combinatorial theory of…
The -positivity of basic Eulerian polynomials via group actions
Zhicong Lin, Jiang Zeng
We provide combinatorial interpretation for the -coefficients of the basic Eulerian polynomials that enumerate permutations by the excedance statistic and the major index as wel…
A curious polynomial interpolation of Carlitz-Riordan's -ballot numbers
Frédéric Chapoton, Jiang Zeng
We study a polynomial sequence defined as a solution of a -difference equation. This sequence, evaluated at -integers, interpolates Carlitz-Riordan's -ballot nu…
Basic and bibasic identities related to divisor functions
Victor J. W. Guo, Jiang Zeng
Using basic hypergeometric functions and partial fraction decomposition we give a new kind of generalization of identities due to Uchimura, Dilcher, Van Hamme, Prodinger, and Chen-…
A one-parameter generalization of Pfaffians
Theresia Eisenkölbl, Masao Ishikawa, Jiang Zeng
In analogy to the definition of the lambda-determinant, we define a one-parameter deformation of the Dodgson condensation formula for Pfaffians. We prove that the resulting rationa…
Positivity properties of Jacobi-Stirling numbers and generalized Ramanujan polynomials
Zhicong Lin, Jiang Zeng
Generalizing recent results of Egge and Mongelli, we show that each diagonal sequence of the Jacobi-Stirling numbers $\js(n,k;z)$ and $\JS(n,k;z)$ is a Pólya frequency sequence if…
A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials
Victor J. W. Guo, Masao Ishikawa, Hiroyuki Tagawa +1
We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of t…
A generalization of the Mehta-Wang determinant and Askey-Wilson polynomials
Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng
Motivated by the Gaussian symplectic ensemble, Mehta and Wang evaluated the by determinant in 2000. When , Ciucu and Krattenthaler computed the…
An expansion formula for the inversions and excedances in the symmetric group
Jiang Zeng
We prove a recent conjecture of Blanco and Petersen (arXiv:1206.0803v2) about an expansion formula for inversions and excedances in the symmetric group.
Two truncated identities of Gauss
Victor J. W. Guo, Jiang Zeng
Two new expansions for partial sums of Gauss' triangular and square numbers series are given. As a consequence, we derive a family of inequalities for the overpartition function $\…
On Zudilin's q-question about Schmidt's problem
Victor J. W. Guo, Jiang Zeng
We propose an elemantary approach to Zudilin's q-question about Schmidt's problem [Electron. J. Combin. 11 (2004), #R22], which has been solved in a previous paper [Acta Arith. 127…
Two new triangles of -integers via -Eulerian polynomials of type and
Guoniu Han, Frédéric Jouhet, Jiang Zeng
The classical Eulerian polynomials can be expanded in the basis () with positive integral coefficients. This formula impl…
A symmetrical q-Eulerian identity
Guoniu Han, Zhicong Lin, Jiang Zeng
We find a -analog of the following symmetrical identity involving binomial coefficients and Eulerian numbers , due to Chung, Graham and Knuth [{\it J. Co…
Jacobi-Stirling polynomials and -partitions
Ira M. Gessel, Zhicong Lin, Jiang Zeng
We investigate the diagonal generating function of the Jacobi-Stirling numbers of the second kind $ \JS(n+k,n;z)$ by generalizing the analogous results for the Stirling and Legendr…
On the number of congruence classes of paths
Zhicong Lin, Jiang Zeng
Let denote the undirected path of length . The cardinality of the set of congruence classes induced by the graph homomorphisms from onto is determined. This…
Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants
Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng
Motivated by the Hankel determinant evaluation of moment sequences, we study a kind of Pfaffian analogue evaluation. We prove an LU-decomposition analogue for skew-symmetric matric…
A q-analogue of Catalan Hankel determinants
Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng
In this paper we shall survey the various methods of evaluating Hankel determinants and as an illustration we evaluate some Hankel determinants of a q-analogue of Catalan numbers.…