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.
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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 -