A dual of MacMahon’s theorem on plane partitions
A dual of MacMahon’s theorem on plane partitions
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麦克马洪平面分割定理的对偶
DOI：
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发表时间：
2012
影响因子：
11.1
通讯作者：
C. Krattenthaler
中科院分区：
文献类型：
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作者：
Mihai Ciucu;C. Krattenthaler
麦克马洪的经典定理指出，在三角晶格上绘制的任何中心对称六边形的菱形平铺数量都由一个精美简单的乘积公式给出。在本文中，我们提出了该公式的对应形式，对应于在绘制每条边后旋转 120° 获得的凹六边形的外部（麦克马洪六边形是通过在每个步骤后旋转 60° 获得的）。
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° after drawing each side (MacMahon’s hexagon is obtained by turning 60° after each step).