On the extremal aspect of the Frobenius problem
type: Item
instance of: scholarly article
title: On the extremal aspect of the Frobenius problem
zbMATH Open document ID: 0853.11020
published in: Journal of Combinatorial Theory. Series A
publication date: 1996-05-13T00:00:00Z
review text: Concerning the Frobenius number \(g= g(a_1, \dots, a_n)\) (cf. the review above) \textit{P. Erdös} and \textit{R. L. Graham} [Acta Arith. 21, 399-408 (1972; Zbl 0246.10010)] defined \(g(n, \ell)= \max_{a_n= \ell} g\), the maximum being taken over all sets of \(n\) coefficients with the maximal coefficient \(\ell\) \((\ell \geq n)\). It is known that \(g(n, \ell)= 2(\ell- n)-1\) if \(\ell \leq 2n- 1\), and \(g(n, 2n)= 2n +1\). In this paper it is shown for \(2n< \ell\leq 3n-2\) \[ g(n, \ell)= \begin{cases} 2(2\ell- 3n)+1 &\quad \text{if } \ell\not\equiv 2\bmod 3\\ 2(2\ell- 3n)-1 &\quad \text{if } \ell\equiv 2 \bmod 3.\end{cases} \] {}.
Mathematics Subject Classification ID: 11D04
zbMATH DE Number: 842833
zbMATH Keywords: Frobenius problem
zbMATH Keywords: Frobenius number
author: Vsevolod F. Lev
reviewed by: Joachim Piehler
MaRDI profile type: Publication
full work available at URL: jcta.1996.0005
OpenAlex ID: W1970410060
DOI: 10.1006/JCTA.1996.0005
description: scientific article; zbMATH DE number 842833