Acta Mathematica Hungarica
Volume/Issue:
Volume 131: Issue 4
Zero-sum problems with congruence conditions
Authors:
Alfred Geroldinger Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstrasse 36, 8010 Graz, Austriae-mails: diambri@hotmail.com, alfred.geroldinger@uni-graz.at

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David J. Grynkiewicz Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstrasse 36, 8010 Graz, Austriae-mails: diambri@hotmail.com, alfred.geroldinger@uni-graz.at

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Wolfgang A. Schmid CMLS, École polytechnique, 91128 Palaiseau cedex, France

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Pages:
323–345
Online Publication Date:
25 Feb 2011
Publication Date:
01 Jun 2011
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-011-0073-7
Keywords:
zero-sum sequence; Erdős–Ginzburg–Ziv constant; Davenport constant; 11B30; 11P70; 20K01
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Abstract

For a finite abelian group G and a positive integer d, let sdℕ(G) denote the smallest integer ℓ∊ℕ0 such that every sequence S over G of length |S|≧ℓ has a nonempty zero-sum subsequence T of length |T|≡0 mod d. We determine sdℕ(G) for all d≧1 when G has rank at most two and, under mild conditions on d, also obtain precise values in the case of p-groups. In the same spirit, we obtain new upper bounds for the Erdős–Ginzburg–Ziv constant provided that, for the p-subgroups Gp of G, the Davenport constant D(Gp) is bounded above by 2exp  (Gp)−1. This generalizes former results for groups of rank two.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
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ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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