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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…