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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 (who called it the tableau algebra), using an operation given by in his study of the longest increasing subsequence of a permutation. It was named the "''monoïde plaxique''" by , 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 the action of a generator of the plactic monoid resembles plates sliding past each other in an earthquake. ==Definition== The plactic monoid over some totally ordered alphabet (often the positive integers) is the monoid with the following presentation: *The generators are the letters of the alphabet *The relations are the elementary Knuth transformations ''yzx'' = ''yxz'' whenever ''x'' < ''y'' ≤ ''z'' and ''xzy'' = ''zxy'' whenever ''x'' ≤ ''y'' < ''z''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Plactic monoid」の詳細全文を読む スポンサード リンク
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