Subsequence containment by involutions

Details Subsequence containment by involutions Subsequence containment by involutions

2001-07-18

arxiv.org/abs/math/0107130v2

Mathematics

Combinatorics

Added section 3.1 on classifying permutations using subsequence containment by involutions, revised history of related work. 1

Scientific paper

Inspired by work of McKay, Morse, and Wilf, we give an exact count of the involutions in S_n which contain a given permutation \tau in S_k as a subsequence; this number depends on the patterns of the first j values of \tau for 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 \tau_1...\tau_k is layered iff, for 1<=j<=k, the pattern of \tau_1...\tau_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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