General Cycling Operations in Garside Groups
نویسندگان
چکیده
In this article, we introduce the notion of cycling operations of arbitrary order in Garside groups, which is a full generalization of the cycling and decycling operations. Theoretically, this notion together with other related concepts provides a context in which various definitions and arguments concerning Garside groups are unified and simplified as well as improved. Practically, it yields a further refined summit set and an algorithm which has a considerably improved performance on solving the conjugacy problem of reducible braids.
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...
متن کاملThe cyclic sliding operation in Garside groups
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 c...
متن کاملA New Approach to the Conjugacy Problem in Garside Groups
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...
متن کاملParabolic subgroups of Garside groups
A Garside monoid is a cancellative monoid with a finite lattice generating set; a Garside group is the group of fractions of a Garside monoid. The family of Garside groups contains the Artin-Tits groups of spherical type. We generalise the well-known notion of a parabolic subgroup of an Artin-Tits group into that of a parabolic subgroup of a Garside group. We also define the more general notion...
متن کاملAn Introduction to Combinatorial Garside Structures
The notion of a Garside group was first introduced in a paper of Dehornoy and Paris [14]. Over the past decade they have been used as a tool to better understand the structure of Artin’s braid groups [2] and their generalizations. In general, one can use the Garside structure associated with a Garside group to solve the word and conjugacy problems, as well as create a finite dimensional Eilenbe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008