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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)

- Georgia Benkart, Caroline Klivans
- 2016

Two classes of avalanche-finite matrices and their critical groups (integer cokernels) are studied from the viewpoint of chip-firing/sandpile dynamics, namely, the Cartan matrices of finite root systems and the McKay-Cartan matrices for finite subgroups G of general linear groups. In the root system case, the recurrent and superstable configurations are… (More)

- Georgia Benkart, Mirna Džamonja, Judith Roitman, Steven G Krantz, Gary Gruenhage, Jan Van Mill +5 others
- 2015

editor of the Notices, invited the editors of this article to prepare a collective remembrance celebrating Mary Ellen Rudin's life and work. In doing so, we asked several of Mary Ellen's colleagues, collaborators, and students to each contribute a short piece. The choice of contributors was not an easy one, since Mary Ellen had a very rich mathematical and… (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)

The nonelliptic A 2-webs with k " + " s on the top boundary and 3n − 2k " − " s on the bottom boundary combinatorially model the space Hom sl 3 (V ⊗(3n−2k) , V ⊗k) of sl 3-module maps on tensor powers of the natural 3-dimensional sl 3-module V, and they have connections with the combinatorics of Springer varieties. Petersen, Pylyavskyy, and Rhodes showed… (More)

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