The extent to which subsets are additively closed

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

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

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 is an element of S) may range between 0 and vertical bar S vertical bar(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/pZ under addition (p prime). We obtain various bounds and results. In the Z/pZ setting, this work may be viewed as a subset generalization of the Cauchy-Daven port Theorem. (C) 2008 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)831-843
Number of pages13
JournalJournal of Combinatorial Theory, Series A
Volume116
Issue number4
DOIs
Publication statusPublished - May 2009

Keywords

  • Finite field
  • Integers modulo p
  • Sum-free set
  • Cauchy-Davenport theorem

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