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Polynomiality of factorizations in reflection groups

Part of: Combinatorics Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 December 2021

Elzbieta Polak  and
Dustin Ross
Elzbieta Polak
Affiliation:
Department of Mathematics, University of Texas at Austin, Austin, TX, USA e-mail: epolak@utexas.edu
Dustin Ross*
Affiliation:
Department of Mathematics, San Francisco State University, San Francisco, CA, USA
*
e-mail: rossd@sfsu.edu
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Abstract

We study the number of ways of factoring elements in the complex reflection groups $G(r,s,n)$ as products of reflections. We prove a result that compares factorization numbers in $G(r,s,n)$ to those in the symmetric group $S_n$ , and we use this comparison, along with the Ekedahl, Lando, Shapiro, and Vainshtein (ELSV) formula, to deduce a polynomial structure for factorizations in $G(r,s,n)$ .

Keywords

Reflection groupsfactorizationsELSV formulapolynomiality

MSC classification

Primary: 20F55: Reflection and Coxeter groups
Secondary: 05A15: Exact enumeration problems, generating functions
Type
Article
Information
Canadian Journal of Mathematics , Volume 75 , Issue 1 , February 2023 , pp. 245 - 266
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Copyright
© Canadian Mathematical Society, 2021

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