The last distribution-equivalence class of mesh patterns of length 2

Zuo-Ru Zhang; Hongkuan Zhao

The last distribution-equivalence class of mesh patterns of length 2

Combinatorics 2026-07-05 v1

Authors: Zuo-Ru Zhang , Hongkuan Zhao

Abstract

We prove the remaining conjectural distribution-equivalence of mesh patterns of length 2 from 2019. This completes the classification of distribution-equivalence and Wilf-equivalence classes for mesh patterns of length 2. Consequently the numbers of such classes are 105 and 46, respectively. We approach this by constructing a marked occurrence bijection, in the spirit of the cluster method for consecutive patterns.

Keywords

mesh patterns distribution-equivalence Wilf-equivalence marked occurrence bijection cluster method consecutive patterns

Cite

@article{arxiv.2607.04111,
  title  = {The last distribution-equivalence class of mesh patterns of length 2},
  author = {Zuo-Ru Zhang and Hongkuan Zhao},
  journal= {arXiv preprint arXiv:2607.04111},
  year   = {2026}
}

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5 pages