Sur une conjecture de Dehornoy
Résumé
Let Mn be the n!×n! matrix indexed by permutations of View the MathML source, defined by Mn(σ,τ)=1 if every descent of τ−1 is also a descent of σ, and Mn(σ,τ)=0 otherwise. We prove the following result, conjectured by P. Dehornoy: let Pn(x) be the characteristic polynomial of Mn. Then, Pn(x) divides Pn+1(x) in View the MathML source.