Proof of a conjecture on the shape-Wilf-equivalence for partially ordered patterns
Abstract
A partially ordered pattern (abbreviated POP) is a partially ordered set (poset) that generalizes the notion of a pattern when we are not concerned with the relative order of some of its letters. The notion of partially ordered patterns provides a convenient language to deal with large sets of permutation patterns. In analogy to the shape-Wilf-equivalence for permutation patterns, Burstein-Han-Kitaev-Zhang initiated the study of the shape-Wilf-equivalence for POPs which would result in the shape-Wilf-equivalence for large sets of permutation patterns. The main objective of this paper is to confirm a recent intriguing conjecture posed by Burstein-Han-Kitaev-Zhang concerning the shape-Wilf-equivalence for POPs of length . This is accomplished by establishing a bijection between two sets of pattern-avoiding transversals of a given Young diagram.
Cite
@article{arxiv.2503.22098,
title = {Proof of a conjecture on the shape-Wilf-equivalence for partially ordered patterns},
author = {Lintong Wang and Sherry H. F. Yan},
journal= {arXiv preprint arXiv:2503.22098},
year = {2025}
}