Subsequence containment by involutions
摘要
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 which contain a fixed tableau of size as a subtableau.
引用
@article{arxiv.math/0107130,
title = {Subsequence containment by involutions},
author = {Aaron D. Jaggard},
journal= {arXiv preprint arXiv:math/0107130},
year = {2007}
}
备注
Added section 3.1 on classifying permutations using subsequence containment by involutions, revised history of related work. 14 pages, 1 figure, 5 tables