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arXiv · 1606.08970

The rotating normal form of braids is regular

Jean Fromentin
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Abstract

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 $\sigma$-definite normal form defined on the whole braid group.

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Jean Fromentin. 2016-06-29. The rotating normal form of braids is regular. https://doi.org/10.1016/j.jalgebra.2018.01.001

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