1. Sur une conjecture de Dehornoy
- Author
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Jean-Yves Thibon, Florent Hivert, Jean-Christophe Novelli, Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), Normandie Université (NU), Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), ANR-06-BLAN-0380,HOPFCOMBOP,Algèbres de Hopf combinatoires, opérades et props(2006), and Thibon, Jean-Yves
- Subjects
Mathematics::Operator Algebras ,Mathematics::Rings and Algebras ,010102 general mathematics ,Group Theory (math.GR) ,0102 computer and information sciences ,General Medicine ,20F36, 05A15 ,01 natural sciences ,[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR] ,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO] ,Combinatorics ,010201 computation theory & mathematics ,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] ,FOS: Mathematics ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,0101 mathematics ,Mathematics - Group Theory ,[MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR] ,Mathematics - 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]., 4 pages, in French
- Published
- 2008
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