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Journal Articles International Journal of Algebra and Computation Year : 2016

Quadratic normalisation in monoids

Abstract

In the general context of presentations of monoids, we study normalisation processes that are determined by their restriction to length-two words. Garside's greedy normal forms and quadratic convergent rewriting systems, in particular those associated with the plactic monoids, are typical examples. Having introduced a parameter called the class measuring the complexity of the normalisation of length-three words, we analyse the normalisation of longer words and describe a number of possible behaviours. We fully axiomatise normalisations of class (4, 3), show the convergence of the associated rewriting systems, and characterise those deriving from a Garside family.
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Dates and versions

hal-01141226 , version 1 (10-04-2015)
hal-01141226 , version 2 (11-05-2016)

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Cite

Patrick Dehornoy, Yves Guiraud. Quadratic normalisation in monoids. International Journal of Algebra and Computation, 2016, 26 (5), pp.935-972. ⟨10.1142/S0218196716500399⟩. ⟨hal-01141226v2⟩
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