DMTCS Proceedings, Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001

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The Many Faces of Alternating-Sign Matrices

James Propp


I give a survey of different combinatorial forms of alternating-sign matrices, starting with the original form introduced by Mills, Robbins and Rumsey as well as corner-sum matrices, height-function matrices, three-colorings, monotone triangles, tetrahedral order ideals, square ice, gasket-and-basket tilings and full packings of loops.

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