Counting crucial permutations with respect to monotone patterns
Abstract
Recently, Avgustinovich, Kitaev, and Taranenko defined five types of (k, )-crucial permutations, which are maximal permutations that do not contain an increasing subsequence of length k or a decreasing subsequence of length . Further, Avgustinovich, Kitaev, and Taranenko began the enumeration of the (k, )-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,)-crucial permutations. In this paper, we complete the enumeration that Avgustinovich, Kitaev, and Taranenko began.
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