The Number of Centered Lozenge Tilings of a Symmetric Hexagon
نویسندگان
چکیده
Abstract. Propp conjectured [15] 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.
منابع مشابه
A dual of MacMahon’s theorem on plane partitions
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عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 86 شماره
صفحات -
تاریخ انتشار 1999