Name: Topology of Cayley Graphs Applied to Inverse Additive Problems
Creator: Hamidoune, Yahya Ould
Keywords: Mathematics - Number Theory, Grafs, Teoria de, 11B60, 11B34, 20D60, Grups abelians, Classificació AMS::05 Combinatorics::05C Graph theory, Problemes inversos (Equacions diferencials), Topology, Topologia, 01 natural sciences, Cayley graphs

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Conference object 01 Jan 2010Embargo end date: 01 Jan 2010Publisher:arXiv

Authors: Hamidoune, Yahya Ould;

doi: 10.48550/arxiv.1011.1797

arXiv: 1011.1797

handle: 2099/10390

Topology of Cayley Graphs Applied to Inverse Additive Problems

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Abstract

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.

Peer Reviewed

Related Organizations

Universitat Polite`cnica de Catalunya
Spain

Keywords

Mathematics - Number Theory, Grafs, Teoria de, 11B60, 11B34, 20D60, Grups abelians, Classificació AMS::05 Combinatorics::05C Graph theory, Problemes inversos (Equacions diferencials), Topology, Topologia, Cayley graphs, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs, Inverse problems (Differential equations), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Number Theory (math.NT), :05 Combinatorics::05C Graph theory [Classificació AMS], Abelian groups, :Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs [Àrees temàtiques de la UPC]

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