Some additive applications of the isoperimetric approach

Yahya O. Hamidoune[1]

  • [1] Université Paris 06 UPMC E. Combinatoire 4, place Jussieu 75005 Paris (France)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 6, page 2007-2036
  • ISSN: 0373-0956

Abstract

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Let G be a group and let X be a finite subset. The isoperimetric method investigates the objective function | ( X B ) ∖ X | , defined on the subsets X with | X | ≥ k and | G ∖ ( X B ) | ≥ k , where X B is the product of X by B .In this paper we present all the basic facts about the isoperimetric method. We improve some of our previous results and obtain generalizations and short proofs for several known results. We also give some new applications.Some of the results obtained here will be used in coming papers to improve Kempermann structure Theory.

How to cite

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Hamidoune, Yahya O.. "Some additive applications of the isoperimetric approach." Annales de l’institut Fourier 58.6 (2008): 2007-2036. <http://eudml.org/doc/10368>.

@article{Hamidoune2008,
abstract = {Let $G$ be a group and let $X$ be a finite subset. The isoperimetric method investigates the objective function $|(XB)\setminus X|$, defined on the subsets $X$ with $|X|\ge k$ and $|G\setminus (XB)|\ge k$, where $XB$ is the product of $X$ by $B$.In this paper we present all the basic facts about the isoperimetric method. We improve some of our previous results and obtain generalizations and short proofs for several known results. We also give some new applications.Some of the results obtained here will be used in coming papers to improve Kempermann structure Theory.},
affiliation = {Université Paris 06 UPMC E. Combinatoire 4, place Jussieu 75005 Paris (France)},
author = {Hamidoune, Yahya O.},
journal = {Annales de l’institut Fourier},
keywords = {Addition theorem; Cayley graph; inverse additive theory; addition theorem},
language = {eng},
number = {6},
pages = {2007-2036},
publisher = {Association des Annales de l’institut Fourier},
title = {Some additive applications of the isoperimetric approach},
url = {http://eudml.org/doc/10368},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Hamidoune, Yahya O.
TI - Some additive applications of the isoperimetric approach
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 6
SP - 2007
EP - 2036
AB - Let $G$ be a group and let $X$ be a finite subset. The isoperimetric method investigates the objective function $|(XB)\setminus X|$, defined on the subsets $X$ with $|X|\ge k$ and $|G\setminus (XB)|\ge k$, where $XB$ is the product of $X$ by $B$.In this paper we present all the basic facts about the isoperimetric method. We improve some of our previous results and obtain generalizations and short proofs for several known results. We also give some new applications.Some of the results obtained here will be used in coming papers to improve Kempermann structure Theory.
LA - eng
KW - Addition theorem; Cayley graph; inverse additive theory; addition theorem
UR - http://eudml.org/doc/10368
ER -

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