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Article Dans Une Revue Symmetry Année : 2019

The Root Extraction Problem for Generic Braids


We show that, generically, finding the k-th root of a braid is very fast. More precisely, we provide an algorithm which, given a braid x on n strands and canonical length l, and an integer k>1 , computes a k-th root of x, if it exists, or guarantees that such a root does not exist. The generic-case complexity of this algorithm is O(l(l+n)n3logn) . The non-generic cases are treated using a previously known algorithm by Sang-Jin Lee. This algorithm uses the fact that the ultra summit set of a braid is, generically, very small and symmetric (through conjugation by the Garside element Δ ), consisting of either a single orbit conjugated to itself by Δ or two orbits conjugated to each other by Δ .

Dates et versions

hal-02428538 , version 1 (06-01-2020)



María Cumplido Cabello, Juan González-Meneses, Marithania Silvero. The Root Extraction Problem for Generic Braids. Symmetry, 2019, 11 (11), pp.1327. ⟨10.3390/sym11111327⟩. ⟨hal-02428538⟩
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