TY - JOUR
T1 - Algorithms for Garside calculus
AU - Dehornoy, Patrick
AU - Gebhardt, Volker
PY - 2014
Y1 - 2014
N2 - Garside calculus is the common mechanism that underlies a certain type of normal form for the elements of a monoid, a group, or a category. Originating from Garside's approach to Artin's braid groups, it has been extended to more and more general contexts, the latest one being that of categories and what are called Garside families. One of the benefits of this theory is to lead to algorithms solving effectively the naturally occurring problems, typically the Word Problem. The aim of this paper is to present and solve these algorithmic questions in the new extended framework.
AB - Garside calculus is the common mechanism that underlies a certain type of normal form for the elements of a monoid, a group, or a category. Originating from Garside's approach to Artin's braid groups, it has been extended to more and more general contexts, the latest one being that of categories and what are called Garside families. One of the benefits of this theory is to lead to algorithms solving effectively the naturally occurring problems, typically the Word Problem. The aim of this paper is to present and solve these algorithmic questions in the new extended framework.
UR - http://handle.uws.edu.au:8081/1959.7/538574
U2 - 10.1016/j.jsc.2013.11.001
DO - 10.1016/j.jsc.2013.11.001
M3 - Article
SN - 0747-7171
VL - 63
SP - 64
EP - 116
JO - Journal of Symbolic Computation
JF - Journal of Symbolic Computation
ER -