PreprintCC BY 4.0arXiv
A Bijective Proof of an Unbalanced Wilf Equivalence
Abstract
We find a bijection to prove that the set of patterns {3412, 4321} is Wilf-equivalent to the set of patterns {3412, 4231, 45321, 54312}. This provides a bijective proof of an identity recently shown by Azam and Richmond.
Related
- Matchings and shape-Wilf-Equivalence of sets of patterns of length three I: Triples
- Matchings and shape-Wilf-Equivalence of sets of patterns of length three II: Quadruples and Quintuples
- Existence, Equivalence, and Convergence of Unbalanced Optimal Transport
- A direct proof of the equivalence of the A2 and the Helson--Szego conditions
- Two refined Wilf-equivalences for patterns of length 4 and a conjecture on Dumont permutations of the first kind
BibTeX
@misc{bridges2026bijective,
title = {{A Bijective Proof of an Unbalanced Wilf Equivalence}},
author = {Jensen Bridges and Michael Waite},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.21684},
eprint = {2608.21684},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.21684},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Bijective Proof of an Unbalanced Wilf Equivalence
AU - Jensen Bridges
AU - Michael Waite
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2608.21684
UR - https://arxiv.org/abs/2608.21684
AB - We find a bijection to prove that the set of patterns {3412, 4321} is Wilf-equivalent to the set of patterns {3412, 4231, 45321, 54312}. This provides a bijective proof of an identity recently shown by Azam and Richmond.
ER -