Extremal Problems on the Hypercube and the Codegree Turán Density of Complete $r$-Graphs
Extremal Problems on the Hypercube and the Codegree Turán Density of Complete $r$-Graphs
Let $G$ be a finite abelian group, and let $r$ be a multiple of its exponent. The generalized Erdös--Ginzburg--Ziv constant $s_r(G)$ is the smallest integer $s$ such that every sequence of length $s$ over $G$ has a zero-sum subsequence of length $r$. We show that $s_{2m}(\mathbb{Z}_2^d) \leq C_m 2^{d/m} + …