Topology of Cayley Graphs Applied to Inverse Additive Problems

Details Topology of Cayley Graphs Applied to Inverse Additive Problems Topology of Cayley Graphs Applied to Inverse Additive Problems

2010-11-08

arxiv.org/abs/1011.1797v1

Mathematics

Combinatorics

Scientific paper

We present proofs of the basic isopermetric structure theory, obtaining some new simplified proofs. As an application, we obtain simple descriptions for subsets $S$ of an abelian group with $|kS|\le k|S|-k+1$ or $|kS-rS|- (k+r)|S|,$ where $1\le r \le k.$ These results may be applied to several questions in Combinatorics and Additive Combinatorics (Frobenius Problem, Waring's problem in finite fields and Cayley graphs with a big diameter, ....).

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