The rotating normal form of braids is regular

Jean Fromentin (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

Defined on Birman–Ko–Lee monoids, the rotating normal form has strong connections with the Dehornoy’s braid ordering. It can be seen as a process for selecting between all the representative words of a Birman–Ko–Lee braid a particular one, called rotating word. In this paper we construct, for all n 2, a finite-state automaton which recognizes rotating words on n strands, proving that the rotating normal form is regular. As a consequence we obtain the regularity of a σ-definite normal form defined on the whole braid group.

Mots clés: rotating normal form; dual braid monoid; regular language; automata

Domaines: Théorie des groupes [math.GR]; Informatique et langage [cs.CL]

Jean Fromentin. The rotating normal form of braids is regular. Journal of Algebra, 2018, 501, pp.545-570. ⟨10.1016/j.jalgebra.2018.01.001⟩. ⟨hal-01337636v3⟩