Refined sign-balance on 321-avoiding permutations
组合数学
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0305327,
title = {Refined sign-balance on 321-avoiding permutations},
author = {Astrid Reifegerste},
journal= {arXiv preprint arXiv:math/0305327},
year = {2007}
}
备注
11 pages