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Tag Archives: words
Free Groups and Tiling
Introduction Consider the following simple problem. Prove that the shape on the left cannot be completely tiled by 20 polygons of the types shown on the right. The solution is rather simple: colour the shape in the following manner. This … Continue reading
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Tagged combinatorics, free groups, group theory, groups, polyominoes, tiling, words
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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 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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