The construction of antipodal triple systems by simulated annealing
type: Item
instance of: scholarly article
title: The construction of antipodal triple systems by simulated annealing
zbMATH Open document ID: 0864.05013
DOI: 10.1016/0012-365X(94)00370-X
author: Peter B. Gibbons
author: Eric Mendelsohn
published in: Discrete Mathematics
publication date: 1997-06-22T00:00:00Z
review text: A Steiner triple system \(S(2,3,v)\) is a pair \((S,B)\), where \(S\) is a \(v\)-set and \(B\) is a set of 3-subsets of \(S\), called triples, such that any pair of distinct elements of \(S\) is included in exactly one triple. A cyclic triple is a directed 3-cycle. A Mendelsohn triple system \(M(2,3,v)\) is a decomposition of the arcs of the complete digraph (without loops) on \(v\) vertices into cyclic triples. A Steiner triple system \((S,B)\) is called hemispheric if there exists an orientation of \(B\) into a set \(B'\) of cyclic triples and an involution \(f\) of \(S\) having exactly one fixed point such that \(B\cap f(B)=\varnothing\) and such that \((S,B'\cup f(B'))\) is a Mendelsohn triple system. The resulting triple \((S,B,f)\) is then called an antipodal triple system. The authors use simulated annealing on a carefully chosen feasibility space to show that any \(S(2,3,v)\) with \(7\leq v\leq15\) is hemispheric. They conjecture that every \(S(2,3,v)\) with \(v>3\) is hemispheric.
reviewed by: Luc Teirlinck
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 932526
zbMATH Keywords: Steiner triple system
zbMATH Keywords: Mendelsohn triple system
zbMATH Keywords: hemispheric
zbMATH Keywords: antipodal triple system
zbMATH Keywords: simulated annealing
zbMATH Keywords: feasibility space
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 932526