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arXiv · 2606.06030

An Erdős-Ko-Rado Theorem for Tilings

Casey Tompkins
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Abstract

We prove an Erdős-Ko-Rado type extremal result for tilings of a $1 \times n$ chessboard by tiles whose lengths belong to a set $Λ$. Two tilings are said to intersect if they contain a tile spanning the same set of squares. We prove that if $1\inΛ$, then the maximum size of an intersecting family of tilings is attained by the set of all tilings containing a fixed singleton tile at one of its ends. This result generalizes a theorem of Butler, Horn and Tressler, which is equivalent to the case $Λ=\{1,2\}$.

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Casey Tompkins. 2026-06-04. An Erdős-Ko-Rado Theorem for Tilings. https://arxiv.org/abs/2606.06030

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