Algorithmic recognition of quasipositive 4-braids of algebraic length three

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).

19 pages, 1 figure

References in corpus (1)

• Algorithmic recognition of quasipositive braids of algebraic length two

Cited by in corpus (2)

• Automorphism group of the commutator subgroup of the braid group
• Quasi-positivity and recognition of products of conjugacy classes in free groups