Olson's constant for the group ℤp⊕ℤp

W. D. Gao, I. Ruzsa, R. Thangadurai

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)49-67
Number of pages19
JournalJournal of Combinatorial Theory, Series A
Volume107
Issue number1
DOIs
Publication statusPublished - Jul 2004

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Subset Sum
Finite Abelian Groups
P-groups
Erdös
Cardinality
Integer
Subset
Zero

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Olson's constant for the group ℤp⊕ℤp. / Gao, W. D.; Ruzsa, I.; Thangadurai, R.

In: Journal of Combinatorial Theory, Series A, Vol. 107, No. 1, 07.2004, p. 49-67.

Research output: Contribution to journalArticle

Gao, W. D. ; Ruzsa, I. ; Thangadurai, R. / Olson's constant for the group ℤp⊕ℤp. In: Journal of Combinatorial Theory, Series A. 2004 ; Vol. 107, No. 1. pp. 49-67.
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