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arXiv · 1504.06612

Algorithmic recognition of quasipositive 4-braids of algebraic length three

Stepan Yu. Orevkov
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Abstract

We give an algorithm to decide whether a given braid with four strings is a product of three factors which are conjugates of standard generators of the braid group. The algorithm is of polynomial time. It is based on the Garside theory. We give also a polynomial algorithm to decide if a given braid with any number of strings is a product of two factors which are conjugates of given powers of the standard generators (in my previous paper this problem was solved without polynomial estimates).

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Stepan Yu. Orevkov. 2015-04-24. Algorithmic recognition of quasipositive 4-braids of algebraic length three. https://doi.org/10.1515/gcc-2015-0012

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