Tilings of Diamonds and Hexagons with Defects

Harald A. Helfgott, Ira M. Gessel


We show how to count tilings of Aztec diamonds and hexagons with defects using determinants. In several cases these determinants can be evaluated in closed form. In particular, we obtain solutions to open problems 1, 2, and 10 in James Propp's list of problems on enumeration of matchings.

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