Stability through non-shadows

2022/12/15 by Jun Gao, Hong Liu, Gao, Jun +3 · 1 citation
Mathematics · #05D05 #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Markov Chains and Monte Carlo Methods #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2212.07821

openalex publication_date 2022/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study families F⊆ 2^[n] with restricted intersections and prove a conjecture of Snevily in a stronger form for large n. 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, which may be of independent interest.

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