A new upper bound for the size of a sunflower-free family

2017/02/09 by Gábor Hegedüs, Hegedüs, Gábor
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.48550/arxiv.1702.02831

11 pages

openalex publication_date 2017/02/09 · arxiv created 2017/03/15 · arxiv updated 2017/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We combine here Tao's slice-rank bounding method and Gröbner basis techniques and apply here to the Erdős-Rado Sunflower Conjecture. Let (3k)/(2)≤ n≤ 3k be integers. We prove that if \cal F be a k-uniform family of subsets of [n] without a sunflower with 3 petals, then |\cal F|≤ 3n \choose n/3. We give also some new upper bounds for the size of a sunflower-free family in 2^[n].

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