Multifraction reduction IV: Padding and Artin--Tits monoids of sufficiently large type

Patrick Dehornoy, Derek F. Holt and Sarah Rees


Artin groups, the word problem, rewriting, multifractions


To appear in J. Pure and Applied Algebra


We investigate the padded version of reduction, an extension of multifraction reduction as defined in arXiv:1606.08991 (to appear), and connect it both with ordinary reduction and with the so-called Property H. As an application, we show that all Artin--Tits groups of sufficiently large type satisfy a weakening Conjecture A(padded) of Conjecture A, thus showing that the reduction approach is relevant for these groups.

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