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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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

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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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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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