论文标题
三角形网格中的三聚体盖：二十个大多是开放的问题
Trimer covers in the triangular grid: twenty mostly open problems
论文作者
论文摘要
在过去的三十年中，对各个平面区域的菱形瓷砖和多米诺骨砖的研究一直是列举组合主义者的蓬勃发展的子场。物理学家将工作归类为有限图的二聚体覆盖物的研究。在本文中，我们超越了二聚体盖的覆盖物，引入了称为苯的平面区域，它们的作用类似于hexagons的菱形瓷砖和用于多米诺骨牌瓷砖的阿兹台克钻石的角色，因为人们发现许多（迄今为止，迄今为止始终是猜想的）确切的票房，构成了瓷砖的数量。
In the past three decades, the study of rhombus tilings and domino tilings of various plane regions has been a thriving subfield of enumerative combinatorics. Physicists classify such work as the study of dimer covers of finite graphs. In this article we move beyond dimer covers to trimer covers, introducing plane regions called benzels that play a role analogous to hexagons for rhombus tilings and Aztec diamonds for domino tilings, inasmuch as one finds many (so far mostly conjectural) exact formulas governing the number of tilings.
