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math.CO2000
Edge Effects on Local Statistics in Lattice Dimers: A Study of the Aztec Diamond (Finite Case)
Harald Helfgott
We compute the probability of any local pattern at an arbitrary position in a random dimer configuration in a square grid with an Aztec-diamond boundary.
math.CO1998
Enumeration of tilings of diamonds and hexagons with defects
Harald 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…