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Tag Archives: skew diagrams
Polynomials and Representations XVIII
Littlewood-Richardson Coefficients Recall that the Littlewood-Richardson coefficient satisfies: By the previous article, for any SSYT of shape , is the number of skew SSYT of shape whose rectification is Since this number is independent of our choice of as long as its shape 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 Littlewood-Richardson 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 XVI
Here is the main problem we are trying to solve today. Word Problem Given a word let us consider disjoint subwords of which are weakly increasing. For example if , then we can pick two or three disjoint subwords as follows: For … Continue reading
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Tagged skew diagrams, sliding algorithm, word problem, words, young tableaux
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Polynomials and Representations XV
Tableaux and Words In our context, a word is a sequence of positive integers; concatenation of words is denoted by Given a skew SSYT the corresponding word is obtained by taking the tableau entries from left to right, then bottom to top. For example the … Continue reading
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Tagged knuth equivalence, skew diagrams, sliding algorithm, words, young tableaux
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Polynomials and Representations XIV
In this article, we describe a way of removing the internal squares of a skew SSYT to turn it into an SSYT. Definition. First write the skew diagram as ; we define an inside corner to be a square in such that there is … Continue reading
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Tagged partitions, skew diagrams, sliding algorithm, young tableaux
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Polynomials and Representations XIII
Skew Diagrams If we multiply two elementary symmetric polynomials and , the result is just , where is the concatenation of and sorted. Same holds for However, we cannot express in terms of easily, which is unfortunate since the Schur functions are the … Continue reading
Mathematics and Such 