Abstract
We get four quartered Aztec diamonds by dividing an Aztec diamond region by two zigzag cuts passing its center. W. Jockusch and J. Propp (in an unpublished work) found that the number of tilings of quartered Aztec diamonds is given by simple product formulas. In this paper we present a simple proof for this result.
Highlights
Propp found that the number of tilings of quartered Aztec diamonds is given by simple product formulas
In this paper we present a simple proof for this result
In this paper a region is a connected union of unit squares in the square lattice
Summary
In this paper a (lattice) region is a connected union of unit squares in the square lattice. The number of tilings of a quartered Aztec diamond is given by the theorem stated below. One can remove some forced edges and the vertices incident to them from a graph to get a new graph with the same number of perfect matchings.
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