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arXiv · 2604.13475

An Erdős-Ko-Rado theorem for binary codes

Shamil Asgarli·Chi Hoi Yip
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Abstract

We study intersecting families of words from the Erdős-Ko-Rado perspective. When the alphabet size is $2$, a maximum intersecting family is not necessarily a star. However, we prove that every maximum $3$-wise intersecting family is a star. We also present a new proof of the known result for alphabets of size at least $3$: maximum intersecting families of words are exactly the stars.

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Shamil Asgarli, Chi Hoi Yip. 2026-04-15. An Erdős-Ko-Rado theorem for binary codes. https://doi.org/10.1017/s0004972726101452

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