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    Involution statistics in finite coxeter groups

    Hart, Sarah and Rowley, P.J. (2014) Involution statistics in finite coxeter groups. Technical Report. Birkbeck College, University of London, London, UK.

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    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) = P 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].


    Item Type: Monograph (Technical Report)
    Additional Information: Birkbeck Mathematical Sciences Preprint Series #4
    Keyword(s) / Subject(s): Coxeter group, permutation statistics, inversions
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Sarah Hart
    Date Deposited: 21 Sep 2015 14:12
    Last Modified: 09 Aug 2023 12:36


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