TY - JOUR

T1 - The extent to which subsets are additively closed

AU - Huczynska, Sophie

AU - Mullen, Gary L.

AU - Yucas, Joseph L.

N1 - Funding Information:
The first author is supported by a Royal Society Dorothy Hodgkin Research Fellowship. We would like to thank the anonymous referees for their suggestions and comments.

PY - 2009/5

Y1 - 2009/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=63249127072&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=63249127072&partnerID=8YFLogxK

U2 - 10.1016/j.jcta.2008.11.007

DO - 10.1016/j.jcta.2008.11.007

M3 - Article

AN - SCOPUS:63249127072

SN - 0097-3165

VL - 116

SP - 831

EP - 843

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 4

ER -