The cyclic sliding operation in Garside groups

By Volker Gebhardt, Juan González-Meneses. 2008

65 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1ca79b97b6800f699187c1c12b95e5246883bc4c

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In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Coherent presentations of Artin monoids (2012, unknown): “We refer to [20] for proofs.”
Foundations of Garside Theory (2013, background): “The operations of transport, which in the terminology of Section 2 is the map on morphisms induced by the sliding fun ctor, and the related operationpullbackwere first introduced in [127] for ultra-summit set, and late r extended to the set of sliding circuits in [129].”
Basic results on braid groups (2010, methodology): “From all these solutions, the easiest to explain, and also the most efficient, is the one explained in detail in [40] using the theoretical results from [39].”