BIROn - Birkbeck Institutional Research Online

    Lengths of Involutions in Finite Coxeter Groups

    Hart, Sarah and Rowley, Peter (2023) Lengths of Involutions in Finite Coxeter Groups. Journal of Pure and Applied Algebra 227 (2), p. 107190. ISSN 0022-4049.

    1-s2.0-S0022404922001864-main.pdf - Published Version of Record
    Available under License Creative Commons Attribution.

    Download (456kB) | Preview


    Let W be a finite Coxeter group and X a subset of W . The length polynomial L_W,X (t) is defined by L_W,X (t) = ∑ x∈X t^{l(x)}, where l is the length function on W. If X = {x ∈ W : x^2 = 1} then we call L_W,X(t) the involution length polynomial of W . In this article we derive expressions for the length polynomial where X is any conjugacy class of involutions, and the involution length polynomial, in any finite Coxeter group W . In particular, these results correct errors in the literature for the involution length polynomials of Coxeter groups of type Bn and Dn.


    Item Type: Article
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Sarah Hart
    Date Deposited: 05 Oct 2022 12:58
    Last Modified: 09 Aug 2023 12:53


    Activity Overview
    6 month trend
    6 month trend

    Additional statistics are available via IRStats2.

    Archive Staff Only (login required)

    Edit/View Item Edit/View Item