Modelling biplanes on surfaces
type: Item
instance of: scholarly article
title: Modelling biplanes on surfaces
zbMATH Open document ID: 1052.05016
published in: European Journal of Combinatorics
publication date: 2004-10-04T00:00:00Z
review text: A biplane is a symmetric design on \(v = k(k-1)/2 + 1\) points and the same number of lines such that (1) each line contains exactly \(k\) points, (2) each point is on exactly \(k\) lines, and (3) any pair of points lie on exactly 2 lines. Non-trivial biplanes are known to exist only for \(k = 3,4,5,6,9,11\), and \(13\). Biplanes can be generated by 2-fold difference sets. In this context, the biplanes can be modeled by embeddings of Cayley graphs on a possibly nonorientable surface or pseudosurface. In this paper the author gives such models for the seven known biplanes generated by difference sets. He asks for suitable topological models for the remaining 10 known biplanes.
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 05B10
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 2105724
zbMATH Keywords: symmetric design
zbMATH Keywords: difference sets
zbMATH Keywords: Cayley graphs
author: Arthur T. White
reviewed by: Dan S. Archdeacon
MaRDI profile type: Publication
full work available at URL: j.ejc.2003.05.004
OpenAlex ID: W1998017106
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DOI: 10.1016/J.EJC.2003.05.004
description: scientific article; zbMATH DE number 2105724