We present the basic isopermetric structure theory, obtaining some new simplified proofs. Let 1 ≤ r ≤ k be integers. As an
application, we obtain simple descriptions for the subsets S of an abelian group with |kS| ≤ k|S|−k+1 or |kS−rS|−(k+r)|S|, where where S denotes as usual the Minkowski sum of copies of S. These results may be applied to several questions in Combinatorics and Additive Combinatorics including the Frobenius Problem, Waring’s problem in finite fields and the structure of abelian Cayley graphs with a big diameter.
CitationHamidoune, Yahya Ould. Topology of Cayley graphs applied to inverse additive problems. A: International Workshop on Optimal Networks Topologies. "Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010". Barcelona: Iniciativa Digital Politècnica, 2011, p. 265-283.
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