Zero-sum problems with subgroup weights
type: Item
instance of: scholarly article
title: Zero-sum problems with subgroup weights
zbMATH Open document ID: 1207.11029
author: Sukumar Das Adhikari
author: A. A. Ambily
author: Balasubramanian Sury
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2010-11-03T00:00:00Z
review text: Given positive integers \(n\) and \(d\), let \(G=({\mathbb Z}_n)^d\) and \(A\subset{\mathbb Z}_n\setminus \{0\}\). Let \(D_A(n,d)\) be the least positive integer \(k\) such that for any sequence \(\{{\mathbf x}_1,\dots,{\mathbf x}_k\}\) of \(k\) elements in \(G\) there exists a non-empty subsequence \(\{{\mathbf x}_{j_1},\dots,{\mathbf x}_{j_t}\}\) and \(a_1,\dots,a_t\) in \(A\) such that \(\sum_{i=1}^t a_i{\mathbf x}_{j_i}={\mathbf 0}\). Similarly, \(f_A(n,d)\) is defined as the least positive integer \(k\) such that for any sequence \(\{{\mathbf x}_1,\dots,{\mathbf x}_k\}\) of \(k\) elements in \(G\) there exists a subsequence \(\{{\mathbf x}_{j_1},\dots,{\mathbf x}_{j_n}\}\) of length \(n\) and \(a_1,\dots,a_n\) in \(A\) with \(\sum_{i=1}^n a_i{\mathbf x}_{j_i}={\mathbf 0}\). These constants generalize the known Davenport constant \(D_A(n,1)\). The aim of the paper is to generalize previous results for \(D_A(n,1)\) and \(f_A(n,1)\) proved by the first author with other coauthors in [Proc. Indian Acad. Sci., Math. Sci. 118, No. 2, 183--188 (2008; Zbl 1207.11030), Integers 6, Paper A30, 6 p., electronic only (2006; Zbl 1107.11018), and Integers 8, No. 1, Article A52, 11 p., electronic only (2008; Zbl 1202.11018)] to general \(d\) with \(n=p\), a prime, and \(A\) a subgroup of \({\mathbb Z}_p^*\).
reviewed by: Štefan Porubský
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 11B13
Mathematics Subject Classification ID: 05D10
Mathematics Subject Classification ID: 05B10
Mathematics Subject Classification ID: 20K01
zbMATH DE Number: 5810046
zbMATH Keywords: Cauchy-Davenport theorem
zbMATH Keywords: Chevalley-Warning problem
zbMATH Keywords: zero-sum problem
zbMATH Keywords: Davenport constant
zbMATH Keywords: Harborth constant
MaRDI profile type: Publication
full work available at URL: s12044-010-0035-y
OpenAlex ID: W2154647468
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DOI: 10.1007/S12044-010-0035-Y
description: scientific article; zbMATH DE number 5810046