The Electronic Journal of Combinatorics
Department of Mathematics
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.
Dartmouth Digital Commons Citation
Elizalde, Sergi, "Fixed Points and Excedances in Restricted Permutations" (2012). Dartmouth Scholarship. 2321.