This material has been published in J. Combin. Theory Ser. A 86 (1999), 103-126, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Academic Press. This material may not be copied or reposted without explicit permission.

Mihai Ciucu and Christian Krattenthaler

The number of centered lozenge tilings of a symmetric hexagon

(19 pages)

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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