Document Type

Article

Publication Date

1-2-2012

Publication Title

The Electronic Journal of Combinatorics

Abstract

Using an unprecedented technique involving diagonals of non-rational generating functions, 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 any given $i,j$. Our theorem generalizes a result of Robertson, Saracino and Zeilberger. Even though bijective proofs have later been found by the author jointly with Pak and with Deutsch, this paper contains the original analytic proof that was presented at FPSAC 2003.

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