Nous présentons un ensemble de conjectures imbriquées qui peuvent être considérées comme des analogues pour l’addition restreinte des théorèmes classiques dûs à Kneser, Kemperman et Scherk. Les connections avec le théorème de Cauchy-Davenport, la conjecture d’Erdős-Heilbronn et la méthode polynomiale d’Alon-Nathanson-Ruzsa sont étudiées.
Cet article ne suppose pas d’expertise de la part du lecteur et peut servir d’introduction au sujet.
We present a system of interrelated conjectures which can be considered as restricted addition counterparts of classical theorems due to Kneser, Kemperman, and Scherk. Connections with the theorem of Cauchy-Davenport, conjecture of Erdős-Heilbronn, and polynomial method of Alon-Nathanson-Ruzsa are discussed.
The paper assumes no expertise from the reader and can serve as an introduction to the subject.
@article{JTNB_2005__17_1_181_0,
author = {Lev, Vsevolod F.},
title = {Restricted set addition in {Abelian} groups: results and conjectures},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {181--193},
publisher = {Universit\'e Bordeaux 1},
volume = {17},
number = {1},
year = {2005},
doi = {10.5802/jtnb.485},
zbl = {1162.11318},
mrnumber = {2152219},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jtnb.485/}
}
TY - JOUR AU - Lev, Vsevolod F. TI - Restricted set addition in Abelian groups: results and conjectures JO - Journal de théorie des nombres de Bordeaux PY - 2005 SP - 181 EP - 193 VL - 17 IS - 1 PB - Université Bordeaux 1 UR - http://www.numdam.org/articles/10.5802/jtnb.485/ DO - 10.5802/jtnb.485 LA - en ID - JTNB_2005__17_1_181_0 ER -
%0 Journal Article %A Lev, Vsevolod F. %T Restricted set addition in Abelian groups: results and conjectures %J Journal de théorie des nombres de Bordeaux %D 2005 %P 181-193 %V 17 %N 1 %I Université Bordeaux 1 %U http://www.numdam.org/articles/10.5802/jtnb.485/ %R 10.5802/jtnb.485 %G en %F JTNB_2005__17_1_181_0
Lev, Vsevolod F. Restricted set addition in Abelian groups: results and conjectures. Journal de théorie des nombres de Bordeaux, Tome 17 (2005) no. 1, pp. 181-193. doi : 10.5802/jtnb.485. http://www.numdam.org/articles/10.5802/jtnb.485/
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