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Pré-Publication, Document De Travail Année : 2015

Quadratic normalisation in monoids

Résumé

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 et versions

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

Identifiants

  • HAL Id : hal-01141226 , version 1

Citer

Patrick Dehornoy, Yves Guiraud. Quadratic normalisation in monoids. 2015. ⟨hal-01141226v1⟩
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