Refined sign-balance on 321-avoiding permutations
| dc.creator | Reifegerste, Astrid | |
| dc.date | 2003-05-23 | |
| dc.date.accessioned | 2026-07-07T04:58:12Z | |
| dc.date.available | 2026-07-07T04:58:12Z | |
| dc.description | The number of even 321-avoiding permutations of length n is equal to the number of odd ones if n is even, and exceeds it by the (n-1)/2th Catalan number otherwise. We present an involution that proves a refinement of this sign-balance property respecting the length of the longest increasing subsequence of the permutation. In addition, this yields a combinatorial proof of a recent analogous result of Adin and Roichman dealing with the last descent. In particular, we answer the question how to obtain the sign of a 321-avoiding permutation from the pair of tableaux resulting from the Robinson-Schensted-Knuth algorithm. The proof of the simple solution bases on a matching method given by Elizalde and Pak. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0305327 | |
| dc.identifier | http://arxiv.org/abs/math/0305327 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67542 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A05 | |
| dc.title | Refined sign-balance on 321-avoiding permutations | |
| dc.type | text |