The many faces of alternating-sign matrices

Abstract

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.

22 pages, 16 figures; presented at "Discrete Models" conference (Paris, July 2001)