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Pré-Publication, Document De Travail Année : 2016

MULTIFRACTION REDUCTION II: CONJECTURES FOR ARTIN-TITS GROUPS

Résumé

Multifraction reduction is a new approach to the Word Problem for Artin-Tits groups and, more generally, for the enveloping group U (M) of a monoid M in which any two elements admit a greatest common divisor. This approach is based on a rewrite system R(M) that extends free group reduction. In this paper, we show that for R(M) to satisfy a weak form of convergence called semi-convergence is sufficient for solving the Word Problem for U (M), and we connect semi-convergence with other conditions involving R(M). We conjecture that all these properties are valid when M is an Artin-Tits monoid, and report about numerical experiments supporting this conjecture.
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Dates et versions

hal-01338095 , version 1 (27-06-2016)
hal-01338095 , version 2 (30-06-2016)
hal-01338095 , version 3 (30-01-2017)

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Patrick Dehornoy. MULTIFRACTION REDUCTION II: CONJECTURES FOR ARTIN-TITS GROUPS. 2016. ⟨hal-01338095v1⟩
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