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arXiv · 2208.13469

Counting crucial permutations with respect to monotone patterns

Yunseo Choi
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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.

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Yunseo Choi. 2022-08-29. Counting crucial permutations with respect to monotone patterns. https://arxiv.org/abs/2208.13469

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