7 papers · 1 filter
A Fixed-Point Worpitzky Identity and a Positive Binomial Transform for Type Involutions
Jiang Zeng
Let be the involutions of the hyperoctahedral group , and let $\des^B$ denote the descent number with respect to the natural Coxeter order. We deriv…
Higher-Order Cyclotomic Congruences for -Secant and Generalized -Euler Numbers
Jiang Zeng
Let $\A(2n)$ denote the set of up--down alternating permutations of , and let \[ E_{2n}(q)=\sum_{σ\in\A(2n)}q^{\operatorname{inv}(σ)}. \] Andrews and Foata prove…
Counting permutations by alternating runs via Hetyei-Reiner trees
Qiongqiong Pan, Yunze Wang, Jiang Zeng
The generating polynomial of permutations of size , counted by the number of alternating runs, has a root at of multiplicity for all . Th…
An involution for trivariate symmetries of vincular patterns
Joanna N. Chen, Shishuo Fu, Jiang Zeng
We provide a bijective proof of the equidistribution of two pairs of vincular patterns in permutations, thereby resolving a recent open problem of Bitonti, Deb, and Sokal (arXiv:24…
Gamma positivity of variations of -Eulerian polynomials
Chao Xu, Jiang Zeng
In 1977 Carlitz and Scoville introduced the cycle -Eulerian polynomials by enumerating permutations with respect to the number of excedanc…
Mahonian-Stirling statistics for partial permutations
Ming-Jian Ding, Jiang Zeng
Recently Cheng et al. (Adv. in Appl. Math. 143 (2023) 102451) generalized the inversion number to partial permutations, which are also known as Laguerre digraphs, and asked for a s…