Improved LP lower bounds for difference triangle sets
type: Item
instance of: scholarly article
title: Improved LP lower bounds for difference triangle sets
zbMATH Open document ID: 0928.05009
author: James B. Shearer
published in: The Electronic Journal of Combinatorics
publication date: 1999-09-19T00:00:00Z
full work available at URL: https://eudml.org/doc/120051
full work available at URL: v6i1r31.html
review text: An \((I,J)\)-difference triangle set is a collection of \(I\) sets \(A_i= \{a_{i0},\dots, a_{ij}\}\) of \(J+1\) integers so that the integers in \(\{a_{ij}- a_{ik}: 1\leq i\leq I\) and \(0\leq k<j\leq J\}\) are all positive and distinct. Then \(M(I,J)\) denotes the minimum over all \((I,J)\)-difference triangle sets. In this paper, an improved linear programming lower bound on \(M(I,J)\) is established. In addition, new optimal constructions are presented when \((I,J)\) is one of \((2, 9)\), \((3, 7)\), \((5, 5)\), and \((9, 4)\).
Mathematics Subject Classification ID: 05B10
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 1334116
zbMATH Keywords: difference triangle sets
zbMATH Keywords: linear programming lower bound
reviewed by: Charles J. Colbourn
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1334116