HARVARD
MATH 126 -
Lecture 10
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The plactic monoidMath 126 Lecture 10ContentsNew definition of a tableau.The word of a tableau.Insertion and bumping.AgainRepeat:Knuth moves.ExampleWhy Knuth moves give slow bumping.Elementary Knuth moves = yKnuth equivalence.Words and tableaux.Web site.Increasing sequences in a word.L(w,k).The word constructed by the bumping algorithm.So as a first step we want to prove thatw w’Removing the largest letter.Proof of the lemma.The plactic monoid.The bumping algorithm for multiplication.The bumping algorithm for multiplication.Multiplication by a rowMultiplication by a row, 2.The bumping route.The bumping routes of multiplication by a row.Multilplication by a column.The plactic monoid.The Pieri
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