3 papers
math.CO2026
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…
math.CO2025
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…
math.CO2025
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…