Sur une conjecture de Dehornoy

Details Sur une conjecture de Dehornoy Sur une conjecture de Dehornoy

2007-10-25

arxiv.org/abs/0710.4792v1

Mathematics

Combinatorics

4 pages, in French

Scientific paper

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].

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