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Bivariate Generating Functions Enumerating Non-Bonding Dominoes on Rectangular Boards

arXiv · Combinatorics(2024)

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Abstract
The manuscript studies configurations of non-overlapping non-bonding dominoes on finite rectangular boards of unit squares characterized by row and column number. The non-bonding dominoes are defined here by the requirement that any domino on the board shares at most one point (one of its four corner points) with any other domino, but no edge. With the Transfer Matrix Method, rational generating functions are derived that solve the enumeration problem entirely, here evaluated for boards with up to six rows or columns.
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要点】:本文研究了在有限长宽的矩形板上,非重叠非绑定多米诺骨牌的配置情况,通过引入双变量生成函数,创新性地解决了计数问题。

方法】:作者使用转移矩阵方法,导出了有理生成函数,以此来完全解决计数问题。

实验】:该研究评估了最多六行或六列的矩形板上的配置情况,但未提及具体的数据集名称和实验结果。