2002/12/16 by Sergi Elizalde, Elizalde, Sergi
Engineering · Mathematics · #05A15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #math.CO #msc:05A15
paper · pdf · doi:10.48550/arxiv.math/0212221
12 pages, 10 figures, submitted to FPSAC'03
arxiv created 2002/12/16 · openalex publication_date 2002/12/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.