Permutations with Extremal number of Fixed Points

Details Permutations with Extremal number of Fixed Points Permutations with Extremal number of Fixed Points

2007-06-12

arxiv.org/abs/0706.1738v2

Mathematics

Combinatorics

minor change about corollary 3

Scientific paper

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.

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