This material has been published in Proc. Natl. Acad. Sci. USA 110 (2013), 4518-4523, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by the National Academy of Sciences of the United States of America. This material may not be copied or reposted without explicit permission.

Mihai Ciucu and Christian Krattenthaler

A dual of MacMahon's theorem on plane partitions

(25 pages)

Abstract. A classical theorem of MacMahon states that the number of lozenge tilings of any centrally symmetric hexagon drawn on the triangular lattice is given by a beautifully simple product formula. In this paper we present a counterpart of this formula, corresponding to the exterior of a concave hexagon obtained by turning 120^o after drawing each side (MacMahon's hexagon is obtained by turning 60^o after each step).

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