[On a conjecture by Dehornoy]
Let be the matrix indexed by permutations of , defined by if every descent of is also a descent of σ, and otherwise. We prove the following result, conjectured by P. Dehornoy: let be the characteristic polynomial of . Then, divides in .
Soit la matrice , indexée par les permutations de , et définie par si toute descente de est aussi une descente de σ, et sinon. Nous démontrons le résultat suivant, conjecturé par P. Dehornoy : soit le polynôme caractéristique de . Alors, divise dans .
Accepted:
Published online:
Florent Hivert 1; Jean-Christophe Novelli 2; Jean-Yves Thibon 2
@article{CRMATH_2008__346_7-8_375_0, author = {Florent Hivert and Jean-Christophe Novelli and Jean-Yves Thibon}, title = {Sur une conjecture de {Dehornoy}}, journal = {Comptes Rendus. Math\'ematique}, pages = {375--378}, publisher = {Elsevier}, volume = {346}, number = {7-8}, year = {2008}, doi = {10.1016/j.crma.2008.02.009}, language = {fr}, }
Florent Hivert; Jean-Christophe Novelli; Jean-Yves Thibon. Sur une conjecture de Dehornoy. Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 375-378. doi : 10.1016/j.crma.2008.02.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.02.009/
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