去除三元组的六边形的镶嵌
Tilings of hexagons with a removed triad of bowties
摘要：
本文考虑了三角形格上任意六边形的问题，该格上有三个任意的蝴蝶结形孔，其中心形成一个等边三角形。这种一般区域的菱形镶嵌的数量是不期望的--实际上也不是-由一个简单的乘积公式给出。然而，当考虑任何这样的区域的某个自然归一化对应物时，我们证明了原始的平铺数与归一化区域的平铺数之间的比率由一个简单的概念性乘积公式给出。几个看似无关的文献结果-包括赖的六边形公式与三个凹痕和Ciucu和Krattenthaler的六边形公式与删除三叶草-遵循我们的结果的直接后果。
英文摘要：
In this paper we consider arbitrary hexagons on the triangular lattice with three arbitrary bowtie-shaped holes, whose centers form an equilateral triangle. The number of lozenge tilings of such general regions is not expected --- and indeed is not --- given by a simple product formula. However, when considering a certain natural normalized counterpart of any such region, we prove that the ratio between the number of tilings of the original and the number of tilings of the normalized region is given by a simple, conceptual product formula. Several seemingly unrelated previous results from the literature --- including Lai's formula for hexagons with three dents and Ciucu and Krattenthaler's formula for hexagons with a removed shamrock --- follow as immediate consequences of our result.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
