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arXiv · 1112.2115

Saturated Domino Coverings

Andrew Buchanan·Tanya Khovanova·Alex Ryba
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Abstract

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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Andrew Buchanan, Tanya Khovanova, Alex Ryba. 2011-12-09. Saturated Domino Coverings. https://arxiv.org/abs/1112.2115

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