Restricted set addition in Abelian groups: results and conjectures
Journal de Théorie des Nombres de Bordeaux, Volume 17 (2005) no. 1, pp. 181-193.

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.

Published online:
DOI: 10.5802/jtnb.485
Vsevolod F. Lev 1

1 Department of Mathematics The University of Haifa at Oranim Tivon 36006, Israel
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Vsevolod F. Lev. 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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.485/

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