2025/05/06 by Ferdinand Ihringer, Ihringer, Ferdinand, Andrey Kupavskii +1
Computer Science · Mathematics · #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #Cooperative Communication and Network Coding #FOS: Mathematics #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2505.03671
openalex publication_date 2025/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The famous Erdős-Rado sunflower conjecture suggests that an s-sun\-flower-free family of k-element sets has size at most (Cs)k for some absolute constant C. In this note, we investigate the analog problem for k-spaces over the field with q elements. For s ≥ k+1, we show that the largest s-sunflower-free family F satisfies 1 ≤ |F| / q^(s-1) \binomk+12 - k ≤ (q/(q-1))k. For s ≤ k, we show that q^-\binomk+12 ≤ |F| / q^(s-1) \binomk+12 - k ≤ (q/(q-1))k. Our lower bounds rely on an iterative construction that uses lifted maximum rank-distance (MRD) codes.