BIROn - Birkbeck Institutional Research Online

    Involution statistics in finite coxeter groups

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

    [img]
    Preview
    Text
    Preprint4Hart.pdf - Draft Version

    Download (1MB) | Preview

    Abstract

    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].

    Metadata

    Item Type: Monograph (Other)
    Keyword(s) / Subject(s): Coxeter group, permutation statistics, inversions
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Sarah Hart
    Date Deposited: 21 Sep 2015 14:12
    Last Modified: 03 Apr 2019 10:07
    URI: http://eprints.bbk.ac.uk/id/eprint/12970

    Statistics

    Downloads
    Activity Overview
    103Downloads
    141Hits

    Additional statistics are available via IRStats2.

    Archive Staff Only (login required)

    Edit/View Item Edit/View Item