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PreprintarXiv licencearXiv

The Hilton-Milner theorem in the ℓ2-norm

  • George Brooks
  • William Linz
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Abstract

The Hilton-Milner theorem is a classical theorem in extremal set theory which determines the maximum size of a nontrivial k-uniform intersecting family. In this paper, we prove an exact version of the Hilton-Milner theorem in the ℓ2-norm. Our method also gives an asymptotic version of the Hilton-Milner theorem in the $(j, p)$-norm.

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Cite

BibTeXRIS
BibTeX
@misc{brooks2026hiltonmilner,
  title = {{The Hilton-Milner theorem in the $\ell_2$-norm}},
  author = {George Brooks and William Linz},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12433},
  eprint = {2610.12433},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12433},
}
RIS
TY  - UNPB
TI  - The Hilton-Milner theorem in the ℓ_2-norm
AU  - George Brooks
AU  - William Linz
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12433
UR  - https://arxiv.org/abs/2610.12433
AB  - The Hilton-Milner theorem is a classical theorem in extremal set theory which determines the maximum size of a nontrivial k-uniform intersecting family. In this paper, we prove an exact version of the Hilton-Milner theorem in the ℓ_2-norm. Our method also gives an asymptotic version of the Hilton-Milner theorem in the $(j, p)$-norm.
ER  -