Alternating normal forms for braids and locally Garside monoids

2007/02/20 by Patrick Dehornoy, Dehornoy, Patrick
Mathematics · #06F05 #20F36 #20M05 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:06F05 #msc:20F36 #msc:20M05

paper · pdf · doi:10.48550/arxiv.math/0702592

arxiv created 2008/02/11 · arxiv updated 2009/12/01

Abstract

We describe new types of normal forms for braid monoids, Artin-Tits monoids, and, more generally, for all monoids in which divisibility has some convenient lattice properties (``locally Garside monoids''). We show that, in the case of braids, one of these normal forms coincides with the normal form introduced by Burckel and deduce that the latter can be computed easily. This approach leads to a new, simple description for the standard ordering (``Dehornoy order'') of Bn in terms of that of B(n-1), and to a quadratic upper bound for the complexity of this ordering.

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