论文标题
Intructions I：普遍入侵
Lozenge Tilings of Hexagons with Intrusions I: Generalized Intrusion
论文作者
论文摘要
麦克马洪关于盒装平面隔板数量的古典定理已在多个方向上概括。概括该定理的一种方法是将盒装平面隔板视为六边形区域的lozenge砖块，然后通过在该地区制造一些孔并计算其瓷砖来概括它。在本文中，我们提供了新区域，其lozenges块的数量由简单的产品配方给出。我们认为的区域可以通过去除称为入侵的结构来从六边形获得。实际上，我们表明，在某些权重下，这些区域的平铺生成功能由相似的公式给出。这些给出了枚举结果的$ q $ - 动态。
MacMahon's classical theorem on the number of boxed plane partitions has been generalized in several directions. One way to generalize the theorem is to view boxed plane partitions as lozenge tilings of a hexagonal region and then generalize it by making some holes in the region and counting its tilings. In this paper, we provide new regions whose numbers of lozenges tilings are given by simple product formulas. The regions we consider can be obtained from hexagons by removing structures called intrusions. In fact, we show that the tiling generating functions of those regions under certain weights are given by similar formulas. These give the $q$-analogue of the enumeration results.
