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RESTRICTED ADDITION IN ${\bb Z}/n {\bb Z}$ AND AN APPLICATION TO THE ERDŐS–GINZBURG–ZIV PROBLEM

Published online by Cambridge University Press:  24 March 2003

L. GALLARDO ,
G. GREKOS ,
L. HABSIEGER ,
F. HENNECART ,
B. LANDREAU  and
A. PLAGNE
L. GALLARDO
Affiliation:
Département de Mathématiques, Université de Brest, 6 Avenue Le Gorgeu, 29285 Brest Cedex, Franceluis.gallardo@univ-brest.fr
G. GREKOS
Affiliation:
Université de Saint-Etienne, Déepartement de Mathématiques, 23 rue du Dr Paul Michelon, 42023 Saint-Etienne Cedex 2, Francegrekos@univ-st-etienne.fr
L. HABSIEGER
Affiliation:
A2X, UMR 5465 CNRS, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence Cedex, Francehabsiege@math.u-bordeaux.frhennec@math.u-bordeaux.frlandreau@math.u-bordeaux.fr
F. HENNECART
Affiliation:
A2X, UMR 5465 CNRS, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence Cedex, Francehabsiege@math.u-bordeaux.frhennec@math.u-bordeaux.frlandreau@math.u-bordeaux.fr
B. LANDREAU
Affiliation:
A2X, UMR 5465 CNRS, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence Cedex, Francehabsiege@math.u-bordeaux.frhennec@math.u-bordeaux.frlandreau@math.u-bordeaux.fr
A. PLAGNE
Affiliation:
LIX, École Polytechnique, 91128 Palaiseau Cedex, Franceplagne@lix.polytechnique.fr
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Abstract

Some elementary results are given on restricted sums $2^{\wedge}{\cal A}$ and $3^{\wedge}{\cal A}$ of a subset ${\cal A}\subset {\bb Z}/n{\bb Z}$ in the case when the cardinality of ${\cal A}$ , is close to $n/2$ . In the last section, some of these results are used to derive some new values of a function related to the Erdős–Ginzburg–Ziv problem.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 65 , Issue 3 , June 2002 , pp. 513 - 523
Copyright
The London Mathematical Society, 2002

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Footnotes

This work has received the support of the CNRS (GDR 495). The sixth author is also supported by the Research Option of the DGA (France).