论文标题
生成狭窄矩形的直聚元瓷砖的功能
Generating functions for straight polyomino tilings of narrow rectangles
论文作者
论文摘要
令$ m，k $固定为正整数。确定$ m \ times n $矩形的砖块数量的生成功能，$ k \ times 1 $矩形是一个长期存在的开放问题，仅在某些特殊情况下答案才知道。在$ M <2k $的情况下，我们为此生成功能提供了明确的公式。此结果用于获得用于$ M \ times n \ times k $ box的砖块数量的生成功能，其中$ k \ times k \ times k \ times 1 $砖块。
Let $m,k$ be fixed positive integers. Determining the generating function for the number of tilings of an $m\times n$ rectangle by $k\times 1$ rectangles is a long-standing open problem to which the answer is only known in certain special cases. We give an explicit formula for this generating function in the case where $m<2k$. This result is used to obtain the generating function for the number of tilings of an $m\times n \times k$ box with $k\times k\times 1$ bricks.
