The well-ordering of dual braid monoids

2007/12/22 by Jean Fromentin, Fromentin, Jean
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.0712.3836

arxiv created 2008/12/10 · arxiv updated 2009/12/01

Abstract

We describe the restriction of the Dehornoy ordering of braids to the dual braid monoids introduced by Birman, Ko and Lee: we give an inductive characterization of the ordering of the dual braid monoids and compute the corresponding ordinal type. The proof consists in introducing a new ordering on the dual braid monoid using the rotating normal form of arXiv:0811.3902 [math.GR], and then proving that this new ordering coincides with the standard ordering of braids.

Citations

• Every braid admits a short sigma-definite representative

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