Solving the conjugacy problem in Garside groups by cyclic sliding

Volker Gebhardt, Juan Gonzalez-Meneses

    Research output: Contribution to journalArticlepeer-review

    15 Citations (Scopus)

    Abstract

    We present a solution to the conjugacy decision problem and the conjugacy search problem in Garside groups, which is theoretically simpler than the usual one, with no loss of efficiency. This is done by replacing the well-known cycling and decycling operations by a new one, called cyclic sliding, which appears to be a more natural choice.We give an analysis of the complexity of our algorithm in terms of fundamental operations with simple elements, so our analysis is valid for every Garside group.This paper intends to be self-contained, not requiring any previous knowledge of prior algorithms, and includes all the details for the algorithm to be implemented on a computer.
    Original languageEnglish
    Pages (from-to)629-656
    Number of pages28
    JournalJournal of Symbolic Computation
    Volume45
    Issue number6
    DOIs
    Publication statusPublished - 2010

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