On a zero-sum generalization of a variation of Schur's equation
type: Item
instance of: scholarly article
title: On a zero-sum generalization of a variation of Schur's equation
zbMATH Open document ID: 1163.05055
author: Arie Bialostocki
author: Rasheed Sabar
author: Daniel Schaal
published in: Graphs and Combinatorics
publication date: 2009-05-08T00:00:00Z
review text: In this paper the authors study a variant of Schur's problem: Let \(m\geq 3\) be a positive integer. Let \(R(L_m;2)\) (or \(R(L_m; \mathbb{Z}_m\)) respectively) denote the minimum integer \(N\) such that for every function \(\Delta:\{1,2, \ldots , N\} \rightarrow \{0,1\}\) (or \(\Delta:\{1,2, \ldots , N\} \rightarrow \mathbb{Z}_m\)) there exist \(m\) integers \(x_1<x_2 < \cdots < x_m\) with \(\sum_{i=1}^{m-1} x_i <x_m\) and \(\Delta(x_1)=\Delta(x_2)= \cdots =\Delta(x_m)\) (and \(\sum_{i=1}^m \Delta(x_i)=0\)). In this paper it is proved that \(R(L_m;2)=R(L_m;\mathbb{Z}_m)\), for every odd prime \(m\). An explicit value of \(R(L_m;2)\) had been worked out in [\textit{A. Bialostocki} and \textit{D. Schaal}, ''On a variation of Schur numbers,'' Graphs Comb. 16, No.\,2, 139-147 (2000; Zbl 0973.05080)].
reviewed by: Christian Elsholtz
Mathematics Subject Classification ID: 05D10
Mathematics Subject Classification ID: 11B50
zbMATH DE Number: 5552217
zbMATH Keywords: Schur's equation
zbMATH Keywords: Erdős-Ginzburg-Ziv theorem
zbMATH Keywords: zerosums
MaRDI profile type: Publication
full work available at URL: s00373-008-0815-7
OpenAlex ID: W2074003206
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DOI: 10.1007/S00373-008-0815-7
description: scientific article; zbMATH DE number 5552217