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Special weight labelings on Aztec diamond graphs lead to sum-product identities through a recursive formula of Kuo. The weight assigned to each perfect matching of the graph is a Laurent monomial, and the identities in these monomials combine to give Weyl's character formula for the representation with highest weight ρ (the half sum of the positive roots)… (More)

We introduce an associative algebra M k (x) whose dimension is the 2k-th Motzkin number. The algebra M k (x) has a basis of " Motzkin diagrams, " which are analogous to Brauer and Temperley-Lieb diagrams, and it contains the Temperley-Lieb algebra TL k (x) as a subalgebra. We prove that for a particular value of x, the algebra M k (x) is the centralizer… (More)

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