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We present a new operation to be performed on elements in a Garside group, called cyclic sliding, which is introduced to replace the well known cycling and decycling operations. Cyclic sliding appears to be a more natural choice, simplifying the algorithms concerning conjugacy in Garside groups and having nicer theoretical properties. We show, in… (More)

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… (More)

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… (More)

The cycling operation is a special kind of conjugation that can be applied to elements in Artin's braid groups, in order to reduce their length. It is a key ingredient of the usual solutions to the conjugacy problem in braid groups. In their seminal paper on braid-cryptography, Ko, Lee et al. proposed the cycling problem as a hard problem in braid groups… (More)

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