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arXiv · 2611.07117

An improved lower bound for maximal partial Room squares

Peter Horak·Dongryul Kim
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Abstract

We establish a new asymptotic lower bound for the volume of a maximal partial Room square of even order $n$. We prove that its volume is at least $\frac{2\sqrt{66}-6}{57}n^2-O(n)$, improving the leading coefficient $1/8$ in the lower bound obtained by Meszka and Rosa. The proof combines two counting arguments, one based on a transversal of empty cells and the other on the graph of occurring symbol pairs.

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Peter Horak, Dongryul Kim. 2026-11-04. An improved lower bound for maximal partial Room squares. https://arxiv.org/abs/2611.07117

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