Two refined Wilf-equivalences for patterns of length 4 and a conjecture on Dumont permutations of the first kind
Year: 2026
Type: preprint
Abstract: We construct a bijection between $2143$-avoiding and $3421$-avoiding permutations that preserves the descent top set and the ascent top set and reverses the left-to-right order of the peaks. This bijection allows us to establish a bijection between $1243$-avoiding and $3412$-avoiding permutations with the same properties. These results refine two cases of a conjecture posed by Burstein and prove a conjecture posed by Burstein and Jones.
Source: arXiv (Cornell University)
Authors: Zhang, Zuo-Ru, Zhao, Hongkuan
Institution: Hebei Normal University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223394044