Involution Statistics in Finite Coxeter Groups
نویسندگان
چکیده
Let W be a finite Coxeter group and X a subset of W . The length polynomial LW,X(t) is defined by LW,X(t) = ∑ x∈X t `(x), where ` is the length function on W . In this article we derive expressions for the length polynomial where X is any conjugacy class of involutions, or the set of all involutions, in any finite Coxeter group W . In particular, these results correct errors in [6] for the involution length polynomials of Coxeter groups of type Bn and Dn. Moreover, we give a counterexample to a unimodality conjecture stated in [6]. Mathematics Subject Classification: 20F55, 05E15
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