Sur une conjecture de Dehornoy
Combinatorics
2013-02-12 v1 Group Theory
Abstract
Let M_n be the n! * n! matrix indexed by permutations of S_n, defined by M_n(sigma,tau)=1 if every descent of tau^{-1} is also a descent of sigma, and M_n(sigma,tau)=0 otherwise. We prove the following result, conjectured by P. Dehornoy: the characteristic polynomial P_n(x)=|xI-M_n| of M_n divides P_{n+1}(x) in Z[x].
Cite
@article{arxiv.0710.4792,
title = {Sur une conjecture de Dehornoy},
author = {Florent Hivert and Jean-Christophe Novelli and Jean-Yves Thibon},
journal= {arXiv preprint arXiv:0710.4792},
year = {2013}
}
Comments
4 pages, in French