81 citations · 484 across the 73 of their papers we have counts for
4 papers · 1 filter
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…
Some q-analogues of (super)congruences of Beukers, Van Hamme and Rodriguez-Villegas
Victor J. W. Guo, Jiang Zeng
For any odd prime p we obtain q-analogues of Van Hamme's supercongruence: $$ \sum_{k=0}^{\frac{p-1}{2}}{2k\choose k}^3\frac{1}{64^k} \equiv 0 \pmod{p^2} \quad\text{for}\quad p\equi…
Some q-analogues of supercongruences of Rodriguez-Villegas
Victor J. W. Guo, Jiang Zeng
We study different q-analogues and generalizations of the ex-conjectures of Rodriguez-Villegas. For example, for any odd prime p, we show that the known congruence \sum_{k=0}^{p-1}…