Hostname: page-component-cb9f654ff-qc88w Total loading time: 0 Render date: 2025-08-23T02:42:17.373Z Has data issue: false hasContentIssue false
  • English
  • Français

On Restricted Sums

Published online by Cambridge University Press:  09 April 2001

Y. O. HAMIDOUNE ,
A. S. LLADÓ  and
O. SERRA
Y. O. HAMIDOUNE
Affiliation:
UFR 921, E. Combinatoire, Université Pierre et Marie Curie, 4 Place Jussieu, 75005 Paris, France (e-mail: yha@ccr.jussieu.fr)
A. S. LLADÓ
Affiliation:
Dep. Matematica Aplicada i Telematica, Universitat Politècnica de Catalunya, Jordi Girona, 1, 08034 Barcelona, Spain (e-mail: allado@mat.upc.es, oserra@mat.upc.es)
O. SERRA
Affiliation:
Dep. Matematica Aplicada i Telematica, Universitat Politècnica de Catalunya, Jordi Girona, 1, 08034 Barcelona, Spain (e-mail: allado@mat.upc.es, oserra@mat.upc.es)
Get access Rights & Permissions [Opens in a new window]

Abstract

Let G be an abelian group. For a subset A ⊂ G, denote by 2 ∧ A the set of sums of two different elements of A. A conjecture by Erdős and Heilbronn, first proved by Dias da Silva and Hamidoune, states that, when G has prime order, [mid ]2 ∧ A[mid ] [ges ] min([mid ]G[mid ], 2[mid ]A[mid ] − 3).

We prove that, for abelian groups of odd order (respectively, cyclic groups), the inequality [mid ]2 ∧ A[mid ] [ges ] min([mid ]G[mid ], 3[mid ]A[mid ]/2) holds when A is a generating set of G, 0 ∈ A and [mid ]A[mid ] [ges ] 21 (respectively, [mid ]A[mid ] [ges ] 33). The structure of the sets for which equality holds is also determined.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 9 , Issue 6 , November 2000 , pp. 513 - 518
Copyright
2000 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable