Conjugacy problem for braid groups and Garside groups
نویسندگان
چکیده
منابع مشابه
Conjugacy problem for braid groups and Garside groups
We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented by Birman, Ko and Lee [3]. This algorithm can be applied not only to braid groups, but to all Garside groups (which include finite type Artin groups and torus knot groups among others).
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The cycling operation endows the super summit set Sx of any element x of a Garside group G with the structure of a directed graph Γx. We establish that the subset Ux of Sx consisting of the circuits of Γx can be used instead of Sx for deciding conjugacy to x in G, yielding a faster and more practical solution to the conjugacy problem for Garside groups. Moreover, we present a probabilistic appr...
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1 We present a solution to the conjugacy decision problem and the conjugacy search problem 2 in Garside groups, which is theoretically simpler than the usual one, with no loss of efficiency. 3 This is done by replacing the well known cycling and decycling operations by a new one, 4 called cyclic sliding, which appears to be a more natural choice. 5 We give an analysis of the complexity of our a...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2003
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(03)00292-8