Hostname: page-component-784d4fb959-pvpmm Total loading time: 0 Render date: 2025-07-14T23:08:20.108Z Has data issue: false hasContentIssue false
  • English
  • Français

On Weighted Sequence Sums

Published online by Cambridge University Press:  12 September 2008

Yahya Ould Hamidoune
Yahya Ould Hamidoune
Affiliation:
E.R. 175 du CNRS “Combinatoire” UFR 921, Université P. et M. Curie, 4 Place Jussieu, 75230 Paris, France
Get access Rights & Permissions [Opens in a new window]

Abstract

The main result of this paper has the following consequence. Let G be an abelian group of order n. Let {xi: 1 ≤ 2n − 1} be a family of elements of G and let {wi: 1 ≤ i ≤ n − 1} be a family of integers prime relative to n. Then there is a permutation & of [1,2n − 1] such that

Applying this result with wi = 1 for all i, one obtains the Erdős–Ginzburg–Ziv Theorem.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 4 , Issue 4 , December 1995 , pp. 363 - 367
Copyright
Copyright © Cambridge University Press 1995

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

References

[1]Alon, N. and Dubriner, M. (1993) Zero-sum sets of prescribed size. In Bolyai, J. (ed.) Combinatorics: Paul Erdős is Eighty; Coll Math. 33–50.Google Scholar
[2]Caro, Y. (to appear) Zero-sum Ramsey problems, a survey. Discrete Math.Google Scholar
[3]Erdős, P., Ginzburg, A. and Ziv, A. (1961) Theorem in additive number theory. Bull. Res. Council, Israel 10.Google Scholar
[4]Mann, H. B. (1967) Two Addition Theorems, Journal of Combinatorial Theory 3 233–235.CrossRefGoogle Scholar
[5]Mann, H. B. (1965) Addition Theorems, Wiley.Google Scholar
[6]Olson, J.E. (1976) A combinatorial problem of Erdős–Ginzburg–Ziv. J. Number Theory 8 52–57.CrossRefGoogle Scholar