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.
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.
@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://archive.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://archive.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://archive.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, Volume 17 (2005) no. 1, pp. 181-193. doi : 10.5802/jtnb.485. http://archive.numdam.org/articles/10.5802/jtnb.485/
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