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Largest Sperner families with bounded VC-dimension — arXiv:2611.06860

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.06860
License (as archived): CC0-1.0
Archived: 2026-11-05T18:28:36.047Z
SHA-256 of the archived text: 33e9b12826e643d96f895b78de4c4ea77f012f6118c5e6003c8b858a6f6b07f3
Stable URL of this page: https://metraipolis.com/documento/dc_eda2f9a91cbf

How to cite

Largest Sperner families with bounded VC-dimension — arXiv:2611.06860 — arXiv (en), https://arxiv.org/abs/2611.06860 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_eda2f9a91cbf (Metraipolis archive dc_eda2f9a91cbf, sha256 33e9b12826e643d96f895b78de4c4ea77f012f6118c5e6003c8b858a6f6b07f3)

BibTeX

@misc{dceda2f9a91cbf,
  title = {Largest Sperner families with bounded VC-dimension — arXiv:2611.06860},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.06860},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_eda2f9a91cbf; sha256 33e9b12826e643d96f895b78de4c4ea77f012f6118c5e6003c8b858a6f6b07f3},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.06860. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A conjecture of Frankl proposed in the 1980s states that for $n\ge2d$, every Sperner family $\mathcal{F}\subseteq 2^{[n]}$ of VC-dimension at most $d$ has at most $\binom{n}{d}$ members. We prove this conjecture for every fixed $d$ and large $n$, and show that equality holds only when $\mathcal{F}$ is $\binom{[n]}{d}$ or $\binom{[n]}{n-d}$.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2611.06860 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-05T18:18:34.002Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).