English

Topology of Cayley Graphs Applied to Inverse Additive Problems

Combinatorics 2010-11-09 v1 Number Theory

Abstract

We present proofs of the basic isopermetric structure theory, obtaining some new simplified proofs. As an application, we obtain simple descriptions for subsets SS of an abelian group with kSkSk+1|kS|\le k|S|-k+1 or kSrS(k+r)S,|kS-rS|- (k+r)|S|, where 1rk.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, ....).

Keywords

Cite

@article{arxiv.1011.1797,
  title  = {Topology of Cayley Graphs Applied to Inverse Additive Problems},
  author = {Yahya Ould Hamidoune},
  journal= {arXiv preprint arXiv:1011.1797},
  year   = {2010}
}