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arXiv · 2111.10669

Finite Coxeter Groups and Generalized Elnitsky Tilings

Robert Nicolaides·Peter Rowley
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Abstract

In [5], Elnitsky constructed three elegant bijections between classes of reduced words for Type $\mathrm{A}$, $\mathrm{B}$ and $\mathrm{D}$ families of Coxeter groups and certain tilings of polygons. This paper offers a particular generalization of this concept to all finite Coxeter Groups in terms of embeddings into the Symmetric Group. [5] Elnitsky, Serge. Rhombic tilings of polygons and classes of reduced words in Coxeter groups. PhD dissertation, University of Michigan, 1993.

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Robert Nicolaides, Peter Rowley. 2021-11-20. Finite Coxeter Groups and Generalized Elnitsky Tilings. https://arxiv.org/abs/2111.10669

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