Subsequence containment by involutions
| dc.creator | Jaggard, Aaron D. | |
| dc.date | 2001-07-18 | |
| dc.date | 2004-09-02 | |
| dc.date.accessioned | 2026-07-07T04:42:38Z | |
| dc.date.available | 2026-07-07T04:42:38Z | |
| dc.description | 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. | |
| dc.description | Added section 3.1 on classifying permutations using subsequence containment by involutions, revised history of related work. 14 pages, 1 figure, 5 tables | |
| dc.identifier | https://arxiv.org/abs/math/0107130 | |
| dc.identifier | http://arxiv.org/abs/math/0107130 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61868 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A05, 05A15, 05E10 | |
| dc.title | Subsequence containment by involutions | |
| dc.type | text |