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articleNo Access
Quadratic normalization in monoids
- Patrick Dehornoy and
- Yves Guiraud
International Journal of Algebra and Computation01 Aug 2016
Preview Abstract
In the general context of presentations of monoids, we study normalization process 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 normalization of length-three words, we analyze the normalization of longer words and describe a number of possible behaviors. We fully axiomatize normalizations of class $(4, 3)$ $(4, 3)$ , show the convergence of the associated rewriting systems, and characterize those deriving from a Garside family.

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