Disjoint odd integer subsets having a constant odd sum
type: Item
instance of: scholarly article
title: Disjoint odd integer subsets having a constant odd sum
zbMATH Open document ID: 0795.05010
DOI: 10.1016/0012-365X(94)90108-2
author: Hung-Lin Fu
author: Wei-Hsin Hu
published in: Discrete Mathematics
publication date: 1994-09-11T00:00:00Z
review text: \textit{K. Ando}, \textit{S. Gervacio} and \textit{M. Kano} [Discrete Math. 82, No. 1, 7-11 (1990; Zbl 0732.05002)] characterized for positive integers \(n\), \(m\), \(k\), systems of \(k\) disjoint nonempty subsets of \(\{1,2, \dots, n\}\) having constant sum \(m\). They also conjectured a characterization of a similar result for \(k\) disjoint nonempty subsets of \(\{1,3,5, \dots, 2n-1\}\). This conjecture was in two parts, according as \(m\) is even or odd. Ando, Gervacio, and Kano announced the even case of their conjecture had been proved by H. Enomoto and M. Kano. The present paper contains a proof of the conjecture when \(m\) is odd.
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 11B75
zbMATH DE Number: 562587
zbMATH Keywords: integer subsets
reviewed by: William G. Brown
MaRDI profile type: Publication
cites work: Disjoint subsets of integers having a constant sum
cites work: Disjoint odd integer subsets having a constant even sum
full work available at URL: 0012-365x(94)90108-2
OpenAlex ID: W2059613815
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description: scientific article; zbMATH DE number 562587