饱和多米诺覆盖
Saturated Domino Coverings
摘要：
如果没有多余的多米诺骨牌，则多米诺骨牌覆盖的电路板是饱和的。我们介绍了一个片段平铺的概念，并表明，一个最小的片段平铺总是对应于一个最大的饱和多米诺覆盖。最小碎片平铺的大小是棋盘的支配数。我们定义了一类定期董事会，并表明，这些董事会的支配数给出了一个最小的X-pentomino覆盖的大小。自然序列计数最大饱和多米诺覆盖的正方形和矩形板。其中包括OEIS的新序列A193764、A193765、A193766、A193767和A193768。
英文摘要：
A domino covering of a board is saturated if no domino is redundant. We introduce the concept of a fragment tiling and show that a minimal fragment tiling always corresponds to a maximal saturated domino covering. The size of a minimal fragment tiling is the domination number of the board. We define a class of regular boards and show that for these boards the domination number gives the size of a minimal X-pentomino covering. Natural sequences that count maximal saturated domino coverings of square and rectangular boards are obtained. These include the new sequences A193764, A193765, A193766, A193767, and A193768 of OEIS.
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