论文标题
五边形的五角形定理
A pentagonal number theorem for tribone tilings
论文作者
论文摘要
康威（Conway）和拉加里亚斯（Lagarias）表明，六角形网格中的某些大致三角形区域不能被形状瑟斯顿（Thurston）铺平，后来被称为部落。在这里，我们研究了六角形网格中大致六角形区域的两参数家族，并表明，当且仅当与该地区相关的两个参数是配对的五角形数字$ k（3k \ pm 1）/2 $时，部落的瓷砖存在。
Conway and Lagarias showed that certain roughly triangular regions in the hexagonal grid cannot be tiled by shapes Thurston later dubbed tribones. Here we study a two-parameter family of roughly hexagonal regions in the hexagonal grid and show that a tiling by tribones exists if and only if the two parameters associated with the region are the paired pentagonal numbers $k(3k \pm 1)/2$.
