论文标题
在三个过路线上有孔的六角形的块状砖块
Lozenge tilings of hexagons with holes on three crossing lines
论文作者
论文摘要
在过去的三十年中，用孔洞列出了hexagons lozenge tiling块。一个值得注意的特征是，最近的许多发展涉及KUO的图形凝结。由Ciucu，Lai和Rohatgi在六角形上进行斜利的工作，并在本文中驱动了六角形的斜利，我们表明，另外两个综合区域的lozenge块数量比例表示为简单的产品配方。我们的证明不涉及图形冷凝法。证明是简短而直接的。我们还提供了一个相应的公式，用于循环对称片片。以前的几个结果可以轻松从我们的概括中得出。
The enumeration of lozenge tilings of hexagons with holes has received much attention during the last three decades. One notable feature is that a lot of the recent development involved Kuo's graphical condensation. Motivated by Ciucu, Lai and Rohatgi's work on tilings of hexagons with a removed triad of bowties, in this paper, we show that the ratio of numbers of lozenge tilings of two more general regions is expressed as a simple product formula. Our proof does not involve the graphical condensation method. The proof is short and direct. We also provide a corresponding formula for cyclically symmetric lozenge tilings. Several previous results can be easily deduced from our generalization.
