Sur une conjecture de Dehornoy
Year: 2007
Type: preprint
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].
Source: arXiv (Cornell University)
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4302436104