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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.22098 |
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Table of Contents:
- 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 $k$. This is accomplished by establishing a bijection between two sets of pattern-avoiding transversals of a given Young diagram.