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arXiv · 1504.02717

Quadratic normalisation in monoids

Patrick Dehornoy·Yves Guiraud
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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 and 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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Patrick Dehornoy, Yves Guiraud. 2016-05-11. Quadratic normalisation in monoids. https://doi.org/10.1142/s0218196716500399

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