Regular Article
The Number of Centered Lozenge Tilings of a Symmetric Hexagon

https://doi.org/10.1006/jcta.1998.2918Get rights and content
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Abstract

Propp conjectured that the number of lozenge tilings of a semiregular hexagon of sides 2n−1, 2n−1, and 2nwhich contain the central unit rhombus is precisely one third of the total number of lozenge tilings. Motivated by this, we consider the more general situation of a semiregular hexagon of sidesa,a, andb. We prove explicit formulas for the number of lozenge tilings of these hexagons containing the central unit rhombus and obtain Propp's conjecture as a corollary of our results.

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Communicated by the Managing Editors

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Current address: School of Mathematics, Georgia Institute of Technology, Skiles Building, 686 Cherry St., Atlanta, GA 30332-0160. E-mail: [email protected].

Research supported in part by the Mathematical Sciences Research Institute.

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E-mail: [email protected]