Skip to Main content Skip to Navigation
Theses

Quelques résultats combinatoires en théorie additive des nombres

Abstract : The first part of this thesis deals with a colouring problem in finite groups. Given a “regular” equation, we focus our interest in the numbers of differently coloured solutions. We express linear relations between these numbers of solutions, that depend only on the cardinalities of the coloured classes and not on the distribution of the colours.
The second part belongs to the range of additive number theory. We develop a new interpretation of the isoperimetric method of Y. ould Hamidoune, which allows us to give a new proof of Kneser's Theorem, which is a major tool in additive number theory. We give another application of this new interpretation to the computation of new values of the size of optimally small sumsets in some non abelian groups. These new values allow us to answer negatively a question asked in litterature.
Document type :
Theses
Complete list of metadatas

Cited literature [31 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00172441
Contributor : Eric Balandraud <>
Submitted on : Monday, September 17, 2007 - 11:13:31 AM
Last modification on : Thursday, January 11, 2018 - 6:12:20 AM
Long-term archiving on: : Friday, April 9, 2010 - 2:16:40 AM

Identifiers

  • HAL Id : tel-00172441, version 1

Collections

CNRS | IMB | INSMI

Citation

Eric Balandraud. Quelques résultats combinatoires en théorie additive des nombres. Mathématiques [math]. Université Sciences et Technologies - Bordeaux I, 2006. Français. ⟨tel-00172441⟩

Share

Metrics

Record views

434

Files downloads

256