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

TL;DR

This paper establishes new upper bounds on the size of certain set systems with restricted intersection properties modulo prime powers, using linear algebra and number theory techniques.

Contribution

It introduces novel upper bounds for set systems with restricted intersections modulo prime powers, expanding understanding in combinatorial set theory.

Findings

Derived upper bounds for set systems with restricted intersections

Applied linear algebra bound method to modular set systems

Utilized number theory in combinatorial bounds

Abstract

Let $q=p^\alpha$ be a fixed prime power, $k\geq 2$ 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 $\{0, \ldots , q-1\}$. Our proof is based on the linear algebra bound method and basic number theory.