A generalization of the Simion-Schmidt bijection for restricted permutations

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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.
8 pages; added results

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Combinatorics, 05A05

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http://salesiana.dossiersoluciones.com/handle/123456789/66183

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0301033
 http://arxiv.org/abs/math/0301033

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arXiv