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The number of centered lozenge tilings of a symmetric hexagon

M. Ciucu·C. Krattenthaler
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Abstract

Propp conjectured that the number of lozenge tilings of a semiregular hexagon of sides $2n-1$, $2n-1$ and $2n$ which 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 sides $a$, $a$ and $b$. 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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M. Ciucu, C. Krattenthaler. 1997-12-01. The number of centered lozenge tilings of a symmetric hexagon. https://arxiv.org/abs/math/9712209

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