81 citations · 484 across the 73 of their papers we have counts for
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Short Proofs of Summation and Transformation Formulas for Basic Hypergeometric Series
Victor J. W. Guo, Jiang Zeng
We show that several terminating summation and transformation formulas for basic hypergeometric series can be proved in a straightforward way. Along the same line, new finite forms…
A Generalization of the Ramanujan Polynomials and Plane Trees
Victor J. W. Guo, Jiang Zeng
Generalizing a sequence of Lambert, Cayley and Ramanujan, Chapoton has recently introduced a polynomial sequence Q_n:=Q_n(x,y,z,t) defined by Q_1=1, Q_{n+1}=[x+nz+(y+t)(n+y\partial…
Factors of Alternating Sums of Products of Binomial and q-Binomial Coefficients
Victor J. W. Guo, Frederic Jouhet, Jiang Zeng
In this paper we study the factors of some alternating sums of products of binomial and q-binomial coefficients. We prove that for all positive integers n_1,...,n_m, n_{m+1}=n_1, a…
Combinatorial Interpretations of the q-Faulhaber and q-Salie Coefficients
Victor J. W. Guo, Martin Rubey, Jiang Zeng
Recently, Guo and Zeng discovered two families of polynomials featuring in a q-analogue of Faulhaber's formula for the sums of powers and a q-analogue of Gessel-Viennot's formula i…
The Andrews-Stanley partition function and Al-Salam-Chihara polynomials
Masao Ishikawa, Jiang Zeng
We show that the sum of the four parameter weights over all ordinary or strict partitions with parts each less than or equal to a given integer is expressed by the Al-Salam Chi…
Some Arithmetic Properties of the q-Euler Numbers and q-Salié Numbers
Victor J. W. Guo, Jiang Zeng
For m>n\geq 0 and 1\leq d\leq m, it is shown that the q-Euler number E_{2m}(q) is congruent to q^{m-n}E_{2n}(q) mod (1+q^d) if and only if m\equiv n mod d. The q-Salié number S_{2n…
The Eulerian Distribution on Involutions is Indeed Unimodal
Victor J. W. Guo, Jiang Zeng
Let I_{n,k} (resp. J_{n,k}) be the number of involutions (resp. fixed-point free involutions) of {1,...,n} with k descents. Motivated by Brenti's conjecture which states that the s…
Applications of Waring's formula to some identities of Chebyshev polynomials
Jiang Zeng, Jin Zhou
Some identities of Chebyshev polynomials are deduced from Waring's formula on symmetric functions. In particular, these formulae generalize some recent results of Grabner and Prodi…
A q-Analogue of Faulhaber's Formula for Sums of Powers
Victor J. W. Guo, Jiang Zeng
Let Generalizing the formulas of Warnaar and Schlosser, we prove that there…
A q-Analog of Dual Sequences with Applications
Sharon J. X. Hou, Jiang Zeng
In the present paper combinatorial identities involving q-dual sequences or polynomials with coefficients q-dual sequences are derived. Further, combinatorial identities for q-bino…