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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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 (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 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/12970 |
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