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In mathematics, the '''plactic monoid''' is the [[monoid]] of all words in the alphabet of positive integers modulo '''Knuth equivalence'''. Its elements can be identified with semistandard Young tableaux. It was discovered by {{harvs|txt|first=Donald|last=Knuth|authorlink=Donald Knuth|year=1970}} (who called it the '''tableau algebra'''), using an operation given by {{harvs|txt|first=Craige|last=Schensted|authorlink=Craige Schensted|year=1961}} in his study of the [[longest increasing subsequence]] of a permutation.
It was named the "''monoïde plaxique''" by {{harvtxt|Lascoux|Schützenberger|1981}}, who allowed any totally ordered alphabet in the definition. The etymology of the word "''plaxique''" is unclear; it may refer to [[plate tectonics]] ("tectonique des plaques" in French), as elementary relations that generate the
==Definition==
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