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The Alternating Normal Form of Braids and Its Minimal Automaton

Authors Vincent Jugé , June Roupin

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Author Details

Vincent Jugé
  • LIGM, CNRS & Univ Gustave Eiffel, Marne-la-Vallée, France
  • IRIF, CNRS & Université Paris Cité, France
June Roupin
  • LIGM, CNRS & Univ Gustave Eiffel, Marne-la-Vallée, France

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Vincent Jugé and June Roupin. The Alternating Normal Form of Braids and Its Minimal Automaton. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 23:1-23:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.AofA.2024.23

Abstract

The alternating normal form of braids is a well-known normal form on standard braid monoids. This normal form is regular: the language it identifies with is regular. We give a characterisation of the minimal automaton of this language and compute its size, both in terms of number of states and of transitions, depending on the number of generators of the monoid.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Enumeration
Keywords
  • Automata
  • braids
  • enumeration
  • normal forms

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