Fon-Der-Flaass, On rainbow arithmetic progressions, Electronic Journal of Combinatorics, vol.11, p.1, 2004. ,
On three-term arithmetic progressions in bicolored sets, preprint, 2005. ,
On the number of monochromatic Schur triples, Advances in Applied Mathematics, vol.31, issue.1, pp.193-198, 2003. ,
DOI : 10.1016/S0196-8858(03)00010-1
A classical introduction to modern number theory, Graduate Texts in Mathematics, vol.84, 1990. ,
Rainbow Arithmetic Progressions and Anti-Ramsey Results, Rainbow Arithmetic Progressions and Anti-Ramsey Results, pp.599-620, 2003. ,
DOI : 10.1017/S096354830300587X
Rainbow 3-term arithmetic progressions, p.18, 2003. ,
Ramsey theory on the integers, Student Mathematical Library, vol.24, 2003. ,
Beweis einer Baudetschen Vermutung, Nieuw Arch, Wisk, vol.15, pp.212-216, 1927. ,
Sums in the grid, Discrete Math, pp.31-48, 1996. ,
Recherches sur les nombres, J. Ecole Polytech, vol.9, pp.99-116, 1813. ,
DOI : 10.1017/CBO9780511702501.004
On the Addition of Residue Classes, Journal of the London Mathematical Society, vol.1, issue.1, pp.30-32, 1935. ,
DOI : 10.1112/jlms/s1-10.37.30
On Kneser's addition theorem in groups, Proc. Amer, pp.38-443, 1973. ,
Permutation groups, 1996. ,
DOI : 10.1007/978-1-4612-0731-3
Sumsets in Vector Spaces over Finite Fields, Journal of Number Theory, vol.71, issue.1, pp.12-39, 1998. ,
DOI : 10.1006/jnth.1998.2235
Optimally small sumsets in finite abelian groups, Journal of Number Theory, vol.101, issue.2, pp.338-348, 2003. ,
DOI : 10.1016/S0022-314X(03)00060-X
Sur les atomes d'un graphe orienté, C.R. Acad. Sci. Paris, vol.284, pp.1253-1256, 1977. ,
On the Connectivity of Cayley Digraphs, European Journal of Combinatorics, vol.5, issue.4, pp.309-312, 1984. ,
DOI : 10.1016/S0195-6698(84)80034-7
On a subgroup contained in some words with a bounded length, Discrete Mathematics, vol.103, issue.2, pp.171-176, 1992. ,
DOI : 10.1016/0012-365X(92)90267-J
An Isoperimetric Method in Additive Theory, Journal of Algebra, vol.179, issue.2, pp.622-630, 1996. ,
DOI : 10.1006/jabr.1996.0028
Subsets with Small Sums in Abelian Groups' I: the Vosper Property, European Journal of Combinatorics, vol.18, issue.5, pp.541-556, 1997. ,
DOI : 10.1006/eujc.1995.0113
Some results in additive number theory I: The critical pair theory, Acta Arithmetica, vol.96, issue.2, pp.97-119, 2000. ,
DOI : 10.4064/aa96-2-1
On small sumsets in an abelian group, Acta Mathematica, vol.103, issue.1-2, pp.63-88, 1960. ,
DOI : 10.1007/BF02546525
Additive number theory sheds extra light on the Hopf-Stiefel ? fonction, L'enseignement Math, pp.109-116, 2003. ,
The critical pairs of subsets of a group of prime order, J. Lond. Math. Soc, pp.31-200, 1956. ,
Addendum to ???The Critical Pairs of Subsets of a Group of Prime Order???, Journal of the London Mathematical Society, vol.1, issue.3, pp.31-280, 1956. ,
DOI : 10.1112/jlms/s1-31.3.280
Orthogonal pairings of Euclidean spaces, Michigan Math, J, vol.28, pp.109-119, 1981. ,
A generalisation to noncommutative groups of a theorem of Mann, Discrete Math, pp.365-372, 1994. ,
Nous allons ici développer un point concernant l'article " The Isoperimetric Method in non-abelian groups with an application to optimally small sumsets " . Dans la section 4.3 de cet article, il est affirmé que pour G un groupe fini et B un sous-ensemble de G, si aucune 1-cellule pour B ne vérifie la condition ,
Proposition 25 Soit M 1 une 1-cellule pour B de taille maximale. Si D B (M 1 ) ne vérifie pas la condition E 1 (B ?1 ), alors pour toute 1-cellule C 1 pour B ,
C 1 telle que M 1 ? C 1 = ?, on a aussi |C 1 | < ? 1 (B ?1 ) De plus, M 1 ? C 1 est une k-cellule avec k 1. Ainsi d'après le lemme 7 ,
En particulier, l = 1 impose que C 1 ? M 1 , car M 1 est une 1-cellule de taille maximale ,