Finite Coxeter Groups and Generalized Elnitsky Tilings

2021/11/20 by Robert Nicolaides, Nicolaides, Robert, Peter Rowley +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2111.10669

openalex publication_date 2021/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In [5], Elnitsky constructed three elegant bijections between classes of reduced words for Type A, B and 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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