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Coxeter groups are biautomatic

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Abstract

We prove that Coxeter groups are biautomatic. From our construction of the biautomatic structure it follows that uniform lattices in isometry groups of buildings are biautomatic.

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  • 02 October 2025

    The original online version of this article was revised: the third affiliation of the first author was missing

Notes

  1. For an equivalent definition, proposed recently by Hohlweg and Parkinson, see [15, Def 4.2 and Prop 4.3].

  2. For a recent shorter proof, see [15, Lem 4.5].

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Acknowledgements

We thank Adrien Abgrall, Pierre-Emmanuel Caprace, Chris Hruska, Jingyin Huang, and Zachary Munro for useful discussions. This paper was written during our stay at the Institut Henri Poincaré in Paris, which we thank for the hospitality.

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Correspondence to Piotr Przytycki.

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The original online version of this article was revised: the third affiliation of the first author was missing

Both authors were partially supported by (Polish) Narodowe Centrum Nauki, UMO-2018/30/M/ST1/00668.

Piotr Przytycki was partially supported by NSERC, AMS, and LabEx CARMIN, ANR-10-LABX-59-01.

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Osajda, D., Przytycki, P. Coxeter groups are biautomatic. Invent. math. 242, 627–637 (2025). https://doi.org/10.1007/s00222-025-01365-6

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