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 language | English |
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Pages (from-to) | 831-843 |
Number of pages | 13 |
Journal | Journal of Combinatorial Theory, Series A |
Volume | 116 |
Issue number | 4 |
DOIs | |
Publication status | Published - May 2009 |
Keywords
- Finite field
- Integers modulo p
- Sum-free set
- Cauchy-Davenport theorem