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arXiv · 2005.00893

Maximum tilings with the minimal tile property

Iwan Praton
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Abstract

A tiling of the unit square is an MTP tiling if the smallest tile can tile all the other tiles. We look at the function $f(n)=\max \sum s_i$, where $s_i$ is the side length of the $i$th tile and the sum is taken over all MTP tilings with $n$ tiles. If $n=k^2+3$, it was conjectured that $f(k^2+3)=k+1/k$. We show that any tiling that violates the conjecture must consist of at least three tile sizes and has exactly one minimal tile.

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Iwan Praton. 2020-05-02. Maximum tilings with the minimal tile property. https://arxiv.org/abs/2005.00893

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