The extent to which subsets are additively closed

Sophie Huczynska, Gary L. Mullen, Joseph L. Yucas

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Given a finite abelian group G (written additively), and a subset S of G, the size r (S) of the set {(a, b) : a, b, a + b ∈ S} may range between 0 and | S |2, with the extremal values of r (S) corresponding to sum-free subsets and subgroups of G. In this paper, we consider the intermediate values which r (S) may take, particularly in the setting where G is Z / p Z under addition (p prime). We obtain various bounds and results. In the Z / p Z setting, this work may be viewed as a subset generalization of the Cauchy-Davenport Theorem.

Original languageEnglish (US)
Pages (from-to)831-843
Number of pages13
JournalJournal of Combinatorial Theory. Series A
Issue number4
StatePublished - May 2009

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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