Permutations with Extremal number of Fixed Points
Combinatorics
2007-06-22 v2
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.
Cite
@article{arxiv.0706.1738,
title = {Permutations with Extremal number of Fixed Points},
author = {Guo-Niu Han and Guoce Xin},
journal= {arXiv preprint arXiv:0706.1738},
year = {2007}
}