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    Commuting Involution Graphs in Classical Affine Weyl Groups

    Hart, Sarah and Sbeiti Clarke, Amal (2018) Commuting Involution Graphs in Classical Affine Weyl Groups. Working Paper. Birkbeck, University of London, London, UK.

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    Abstract

    In this paper we investigate commuting involution graphs in classical affine Weyl groups. Let $W$ be a classical Weyl group of rank $n$, with $\tilde W$ its corresponding affine Weyl group. Our main result is that if $X$ is a conjugacy class of involutions in $\tilde W$, then the commuting involution graph $\C(\tilde W, X)$ is either disconnected or has diameter at most $n+2$. This bound is known to hold for types $\tilde A_n$ and $\tilde C_n$, so the main work of this paper is to prove the theorem for types $\tilde B_n$ and $\tilde D_n$.

    Metadata

    Item Type: Monograph (Working Paper)
    Additional Information: Mathematical Sciences Preprint Series No.43
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Sarah Hart
    Date Deposited: 17 Sep 2018 12:52
    Last Modified: 21 Jul 2020 19:48
    URI: http://eprints.bbk.ac.uk/id/eprint/23909

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