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Geodesic automation and growth functions for Artin groups of finite type. (English) Zbl 0813.20042
For an Artin group (or generalized braid group) associated to a finite Coxeter group, we exhibit an automatic structure whose language is symmetric, geodesic and one-to-one. Using this automatic structure, we show how to explicitly compute rational growth functions for these groups.

MSC:
20F36 Braid groups; Artin groups
20F65 Geometric group theory
20F05 Generators, relations, and presentations of groups
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
20F55 Reflection and Coxeter groups (group-theoretic aspects)
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