标题： 计数不同的二聚体六边形铺砌 显示英文标题

标题： Counting distinct dimer hex tilings

摘要： 六边形的整数边长为$n$的铺砌问题，由边长为1的120度-60度菱形铺砌的组合学有着悠久的历史，直接（作为热力学模型中的一个感兴趣的问题）和间接（通过与平面分拆的等价性）。对于六边形每种对称性的此类铺砌数量，已经提出了公式，并逐一得到了证明。然而，当撰写本注释时，OEIS（在线整数序列百科全书）中关于不同此类铺砌数量的条目仅包含$0 \le n \le 4$的表格和对该数值的简要讨论。本文的目的是汇集相关事实。 显示英文摘要

摘要： The combinatorics of tilings of a hexagon of integer side-length $n$ by 120 degree - 60 degree diamonds of side-length 1 has a long history, both directly (as a problem of interest in thermodynamic models) and indirectly (through the equivalence to plane partitions). Formulae as products of factorials have been conjectured and, one by one, proven for the number of such tilings under each of the symmetries of the hexagon. However, when this note was written the entry for the number of distinct such tilings in the Online Encyclopedia of Integer Sequences (OEIS) consisted of little more than a table for $0 \le n \le 4$ and a brief discussion of those values. The aim of this note is to pull together the relevant facts.