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Tag Archives: rsk correspondence
Polynomials and Representations XX
From now onwards, we will assume the base field K has characteristic 0. Example: d=3 Following the previous article, we examine the case of . We get 3 partitions: , and Let us compute for all From the previous article, we have: Since , is … Continue reading
Polynomials and Representations XVII
Two Important Results In this article and the next, we will find a combinatorial way of computing the LittlewoodRichardson coefficient. The key result we have so far is that given any word w there is a unique SSYT T (called the rectification of … Continue reading
Polynomials and Representations IX
Hall Inner Product Let us resume our discussion of symmetric polynomials. First we define an inner product on dth component of the formal ring. Recall that the sets are both bases of . Definition. The Hall inner product is defined by setting and to be … Continue reading
Polynomials and Representations VIII
Matrix Balls Given a matrix A of nonnegative integers, the standard RSK construction masks the symmetry between P and Q, but in fact we have: Symmetry Theorem. If A corresponds to (P, Q), then the transpose of A corresponds to (Q, P). In particular, if A is a … Continue reading
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Tagged combinatorics, matrix balls, partitions, rsk correspondence, young tableaux
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Polynomials and Representations VII
Our next task is as follows: Given partition and vector , count the number of semistandard Young tableaux with shape and type (i.e. occurs times). Proposition. The number of SSYT with shape and type remains invariant when we permute the … Continue reading
Posted in Uncategorized
Tagged combinatorics, partitions, rsk correspondence, symmetric polynomials, young tableaux
Leave a comment