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Generating random braids

By Volker Gebhardt and Juan González-Meneses López

Abstract

We present an algorithm to generate positive braids of a given length as words in Artin generators with a uniform probability. The complexity of this algorithm is polynomial in the number of strands and in the length of the generated braids. As a byproduct, we describe a finite state automaton accepting the language of lexicographically minimal representatives of positive braids that has the minimal possible number of states, and we prove that its number of states is exponential in the number of strands.Australian Research Council’s Discovery ProjectsMinisterio de Ciencia e InnovaciónJunta de AndalucíaFondo Europeo de Desarrollo Regiona

Topics: Random braids, Uniform random generator, Lexicographically minimal representatives, Regular language, Forbidden prefixes, Finite state automata
Publisher: 'Elsevier BV'
Year: 2013
DOI identifier: 10.1016/j.jcta.2012.07.003
OAI identifier: oai:idus.us.es:11441/42263

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