Fixed points and excedances in restricted permutations

Details Fixed points and excedances in restricted permutations Fixed points and excedances in restricted permutations

2002-12-16

arxiv.org/abs/math/0212221v1

Mathematics

Combinatorics

12 pages, 10 figures, submitted to FPSAC'03

Scientific paper

In this paper we prove that among the permutations of length n with i fixed points and j excedances, the number of 321-avoiding ones equals the number of 132-avoiding ones, for all given i,j<=n. We use a new technique involving diagonals of non-rational generating functions. This theorem generalizes a recent result of Robertson, Saracino and Zeilberger, for which we also give another, more direct proof.

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