Counting crucial permutations with respect to monotone patterns

Yunseo Choi

Counting crucial permutations with respect to monotone patterns

Combinatorics 2022-08-30 v1

Authors: Yunseo Choi

Abstract

Recently, Avgustinovich, Kitaev, and Taranenko defined five types of $(k, \ell)-$ crucial permutations, which are maximal permutations that do not contain an increasing subsequence of length $k$ or a decreasing subsequence of length $\ell$ . Further, Avgustinovich, Kitaev, and Taranenko began the enumeration of the $(k, \ell)-$ crucial permutations of the minimal length and the next minimal length and the $(k, 3)-$ crucial permutations of all lengths for each of the five types of $(k,\ell)-$ crucial permutations. In this paper, we complete the enumeration that Avgustinovich, Kitaev, and Taranenko began.

Cite

@article{arxiv.2208.13469,
  title  = {Counting crucial permutations with respect to monotone patterns},
  author = {Yunseo Choi},
  journal= {arXiv preprint arXiv:2208.13469},
  year   = {2022}
}

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