Let G be a finite abelian group. By Ol(G), we mean the smallest integer t such that every subset A⊂G of cardinality t contains a non-empty subset whose sum is zero. In this article, we shall prove that for all primes p>4.67×1034, we have Ol(ℤp ⊕ ℤp)=p+Ol(ℤp)-1 and hence we have Ol(ℤp⊕ ℤp) ≤p-1+⌈2p+5 log p⌉. This, in particular, proves that a conjecture of Erdos (stated below) is true for the group ℤp⊕ ℤp for all primes p>4.67×1034.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics