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The extent to which subsets are additively closed |
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| Authors: | Sophie Huczynska |
| Affiliation: | a School of Mathematics and Statistics, University of St. Andrews, Fife, KY16 9SS, UK b Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA c Department of Mathematics, Southern Illinois University, Carbondale, IL 62901, USA |
| Abstract: | Given a finite abelian group G (written additively), and a subset S of G, the size r(S) of the set  may range between 0 and 2|S|, 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-Davenport Theorem. |
| Keywords: | Finite field Integers modulo p Sum-free set Cauchy-Davenport theorem |
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