New upper bounds for the size of set systems with restricted intersections modulo prime powers

2025/01/06 by Gábor Hegedüs, Hegedüs, Gábor
Computer Science · Mathematics · #05D05 #12D99 #15A03 #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2501.02925

openalex publication_date 2025/01/06 · openalex created_date 2025/01/08 · openalex updated_date 2026/07/28

Abstract

Let q=p^α be a fixed prime power, k≥ 2 be an integer. We give a new upper bound for the size of k-wise q-modular L-avoiding L-intersecting set systems, where L is any proper subset of \0, … , q-1\. Our proof is based on the linear algebra bound method and basic number theory.

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