Abstract:In this paper we enumerate the centrally symmetric lozenge tilings of a hexagon with a shamrock removed from its center. Our proof is based on a variant of Kuo's graphical condensation method in which only three of the four involved vertices are on the same face. As a special case, we obtain a new proof of the enumeration of the self-complementary plane partitions.

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中文翻译：

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三叶草的对称性IV：自我互补的情况

摘要：本文列举了六边形的中心对称菱形平铺，其中三叶草从其中心移开。我们的证明基于Kuo的图形压缩方法的一种变体，其中四个涉及的顶点中只有三个在同一面上。作为一种特殊情况，我们获得了自互补平面分区的枚举的新证明。

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