The cyclic sliding operation in Garside groups
نویسندگان
چکیده
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 particular, that if a super summit element has conjugates which are rigid (that is, which have a certain particularly simple structure), then the optimal way of obtaining such a rigid conjugate through conjugation by positive elements is given by iterated cyclic sliding.
منابع مشابه
Solving the conjugacy problem in Garside groups by cyclic sliding
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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