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 $\stackrel{}{R}$ of any such region R, we prove that the ratio between the number of tilings of R and the number of tilings of $\stackrel{}{R}$ 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 special cases of our result.

在本文中，我们考虑在三角形格子上具有三个任意领结形孔的任意六边形，其中心形成一个等边三角形。这种简单区域的菱形拼贴的数量是不期望的，实际上也不是通过简单的产品公式给出的。但是，当考虑某个自然归一化的对应物时$\stackrel{}{\mathrm{[R}}$任何这样的区域的[R ，证明了的拼接的数目之间的比率[R和拼接的数目$\stackrel{}{\mathrm{[R}}$由一个简单的概念性产品公式给出。以下是文献中一些看似无关的结果-包括赖的三凹痕六角形公式和Ciucu和Krattenthaler的三叶草去除六边形公式-作为我们结果的直接特例。