A generalization of the Simion-Schmidt bijection for restricted permutations
组合数学
2007-05-23 v3
摘要
We consider the two permutation statistics which count the distinct pairs obtained from the last two terms of occurrences of patterns t_1...t_{m-2}m(m-1) and t_1...t_{m-2}(m-1)m in a permutation, respectively. By a simple involution in terms of permutation diagrams we will prove their equidistribution over the symmetric group. As special case we derive a one-to-one correspondence between permutations which avoid each of the patterns t_1...t_{m-2}m(m-1) in S_m and such ones which avoid each of the patterns t_1...t_{m-2}(m-1)m. For m=3, this correspondence coincides with the bijection given by Simion and Schmidt in their famous paper on restricted permutations.
引用
@article{arxiv.math/0301033,
title = {A generalization of the Simion-Schmidt bijection for restricted permutations},
author = {Astrid Reifegerste},
journal= {arXiv preprint arXiv:math/0301033},
year = {2007}
}
备注
8 pages; added results