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Journal Articles Journal of Algebra Year : 2018

The rotating normal form of braids is regular


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.
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Dates and versions

hal-01337636 , version 1 (27-06-2016)
hal-01337636 , version 2 (29-06-2016)
hal-01337636 , version 3 (20-02-2018)



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⟩
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