English

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 22, a maximum intersecting family is not necessarily a star. However, we prove that every maximum 33-wise intersecting family is a star. We also present a new proof of the known result for alphabets of size at least 33: 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

R2 v1 2026-07-01T12:10:06.947Z