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Subsequence containment by involutions

Aaron D. Jaggard
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Abstract

Inspired by work of McKay, Morse, and Wilf, we give an exact count of the involutions in S_n which contain a given permutation τin S_k as a subsequence; this number depends on the patterns of the first j values of τfor 1<=j<=k. We then use this to define a partition of S_k, analogous to Wilf-classes in the study of pattern avoidance, and examine properties of this equivalence. In the process, we show that a permutation τ_1...τ_k is layered iff, for 1<=j<=k, the pattern of τ_1...τ_j is an involution. We also obtain a result of Sagan and Stanley counting the standard Young tableaux of size $n$ which contain a fixed tableau of size $k$ as a subtableau.

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Aaron D. Jaggard. 2004-09-02. Subsequence containment by involutions. https://arxiv.org/abs/math/0107130

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