arXiv:0706.1738 Abstract | arXiv Analytics

arXiv:0706.1738 [math.CO]Abstract References Reviews Resources

Permutations with Extremal number of Fixed Points

Published 2007-06-12, updated 2007-06-22Version 2

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.

Comments: minor change about corollary 3

Categories: math.CO

Subjects: 05A05, 05A15, 05E05

Keywords: extremal number, fixed points, extend stanleys work, alternating permutations, desarmeniens desarrangement combinatorics

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