Permutations with extremal number of fixed points

Authors:
Guo-Niu Han;Guoce Xin
Affiliations:
Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, PR China and I.R.M.A. UMR 7501, Université Louis Pasteur et CNRS, 7 rue René-Descartes, F-67084 Strasbourg, Franc ...;Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, PR China
Venue:
Journal of Combinatorial Theory Series A
Year:
2009

Citing 6
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Abstract

We extend Stanley's work on alternating permutations with extremal number of fixed points in two directions: first, alternating permutations are replaced by permutations with a prescribed descent set; second, instead of simply counting permutations we study their generating polynomials by number of excedances. Several techniques are used: Desarmenien's desarrangement combinatorics, Gessel's hook-factorization and the analytical properties of two new permutation statistics ''DEZ'' and ''lec.'' Explicit formulas for the maximal case are derived by using symmetric function tools.