Generating random braids

Volker Gebhardt; Juan González-Meneses

doi:10.1016/j.jcta.2012.07.003

Generating random braids

Volker Gebhardt, Juan González-Meneses

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

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.

Original language	English
Pages (from-to)	111-128
Number of pages	18
Journal	Journal of Combinatorial Theory, Series A
Volume	120
Issue number	1
DOIs	https://doi.org/10.1016/j.jcta.2012.07.003
Publication status	Published - 2013

Keywords

random braids
finite state automata
forbidden prefixes
regular language

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10.1016/j.jcta.2012.07.003

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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.",

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AB - 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.

KW - random braids

KW - finite state automata

KW - forbidden prefixes

KW - regular language

UR - http://handle.uws.edu.au:8081/1959.7/524463

U2 - 10.1016/j.jcta.2012.07.003

DO - 10.1016/j.jcta.2012.07.003

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SP - 111

EP - 128

JO - Journal of Combinatorial Theory, Series A

JF - Journal of Combinatorial Theory, Series A

IS - 1

ER -

Generating random braids

Abstract

Keywords

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