An Erd\H{o}s-Ko-Rado theorem for binary codes
Combinatorics
2026-04-16 v1
Abstract
We study intersecting families of words from the Erd\H{o}s-Ko-Rado perspective. When the alphabet size is , a maximum intersecting family is not necessarily a star. However, we prove that every maximum -wise intersecting family is a star. We also present a new proof of the known result for alphabets of size at least : maximum intersecting families of words are exactly the stars.
Keywords
Cite
@article{arxiv.2604.13475,
title = {An Erd\H{o}s-Ko-Rado theorem for binary codes},
author = {Shamil Asgarli and Chi Hoi Yip},
journal= {arXiv preprint arXiv:2604.13475},
year = {2026}
}
Comments
short notes, 6 pages