English

Stability through non-shadows

Combinatorics 2023-06-27 v2

Abstract

We study families F2[n]\mathcal{F}\subseteq 2^{[n]} with restricted intersections and prove a conjecture of Snevily in a stronger form for large nn. We also obtain stability results for Kleitman's isodiametric inequality and families with bounded set-wise differences. Our proofs introduce a new twist to the classical linear algebra method, harnessing the non-shadows of F\mathcal{F}, which may be of independent interest.

Keywords

Cite

@article{arxiv.2212.07821,
  title  = {Stability through non-shadows},
  author = {Jun Gao and Hong Liu and Zixiang Xu},
  journal= {arXiv preprint arXiv:2212.07821},
  year   = {2023}
}
R2 v1 2026-06-28T07:36:27.538Z