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On a Combinatorial Theorem of Erdös, Ginzburg and Ziv

Published online by Cambridge University Press:  01 December 1998

YAHYA OULD HAMIDOUNE,
OSCAR ORDAZ and
ASDRUBAL ORTUÑO
YAHYA OULD HAMIDOUNE
Affiliation:
E. R. Combinatoire, UFR 921, Case 189, Université Pierre et Marie Curie, 4 Place Jussieu, 75230 Paris, France (e-mail: yha@ccr.jussieu.fr)
OSCAR ORDAZ
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias Universidad Central de Venezuela, Ap. 47567, Caracas 1041-A, Venezuela (e-mail: oordaz@isys.ciens.ucv.ve)
ASDRUBAL ORTUÑO
Affiliation:
Centro de Ingeniería de Software Y Sistema (ISYS), Facultad de Ciencias Universidad Central de Venezuela, Ap. 47567, Caracas 1041-A, Venezuela (e-mail: asdrubal@anubis.ciens.ucv.ve)
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Abstract

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Let G be an abelian group of order n and let μ be a sequence of elements of G with length 2n−k+1 taking k distinct values. Assuming that no value occurs n−k+3 times, we prove that the sums of the n-subsequences of μ must include a non-null subgroup. As a corollary we show that if G is cyclic then μ has an n-subsequence summing to 0. This last result, conjectured by Bialostocki, reduces to the Erdos–Ginzburg–Ziv theorem for k=2.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 7 , Issue 4 , December 1998, pp. 403 - 412
Copyright
1998 Cambridge University Press