Generating random braids

Details Generating random braids Generating random braids

2011-12-22

arxiv.org/abs/1112.5485v1

Mathematics

Group Theory

22 pages

Scientific paper

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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