Jean Raimbault: Subgroup growth of right-angled groups

Előadó: Jean Raimbault

Cím: Subgroup growth of right-angled groups

Absztrakt: I will discuss asymptotic estimates for the number s_n(\Gamma) of subgroups of index n in a right-angled Artin and Coxeter group \Gamma, a joint work with H. Baik and Bram Petri. In the case of an Artin group we identify the main term of \log(s_n(\Gamma)). In the case of a Coxeter group we conjecture such a result but we are not able to prove that it holds in general. The proofs are essentially combinatorial, as the problem reduces to a counting problem about permutations satisfying certain commutation relations.