Some estimated formulas for the Frobenius numbers
type: Item
instance of: scholarly article
title: Some estimated formulas for the Frobenius numbers
zbMATH Open document ID: 0856.11013
DOI: 10.1016/0024-3795(94)00204-5
author: J. Shen
published in: Linear Algebra and its Applications
publication date: 1996-11-26T00:00:00Z
review text: If \(a_0< a_1< \dots< a_s\) are integers with gcd \((a_0, a_1, \dots, a_s)=1\) and \(a_i \not\equiv a_j \pmod {a_0}\) for any \(i\neq j\), then a generalization of Vitek's bound of the Frobenius number \(g(a_0, a_1, \dots, a_n)\) is given. If \(a_0\) is prime it is shown that \[ g(a_0, a_1, \dots, a_n) \leq \biggl\lfloor {{a_0 -2} \over 2}+1 \biggr\rfloor (a_s- s)- 1. \] Some other bounds are given in the cases \(s=3\) and \(s=2\).
Mathematics Subject Classification ID: 11D04
Mathematics Subject Classification ID: 11B13
zbMATH DE Number: 931936
zbMATH Keywords: linear diophantine equations
zbMATH Keywords: Vitek's bound
zbMATH Keywords: Frobenius number
reviewed by: Joachim Piehler
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00204-5
OpenAlex ID: W1992276146
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description: scientific article; zbMATH DE number 931936