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- W3118132010 abstract "In this article, we prove combinatorial and algebraic properties on the plactic and hypoplactic congruences via a new rewriting approach on tableaux, that we apply to the jeu de taquin and the right-bottom rectification algorithms. The jeu de taquin is an algorithm that transforms a skew tableau into a Young tableau by local transformation rules on the columns of the tableaux. This algorithm has remarkable combinatorial and algorithmic properties, in particular it is confluent, that is the resulting Young tableau does not depend on the way the local transformations rules are applied. We introduce the notion of string of columns rewriting system in order to study rewriting properties of algorithms defined on glued sequences of columns. We prove the convergence of the jeu de taquin and we show how to deduce algebraic properties on the plactic congruence. We define the right-bottom rectification algorithm that transforms a Young tableau into a quasi-ribbon tableau by a string of columns rewriting system. We prove its convergence and we deduce algebraic properties on the hypoplactic congruence." @default.
- W3118132010 created "2021-01-05" @default.
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- W3118132010 date "2020-12-31" @default.
- W3118132010 modified "2023-09-25" @default.
- W3118132010 title "String of columns rewriting and plactic-like data structures" @default.
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