On symmetric Moore geometries
type: Item
instance of: scholarly article
title: On symmetric Moore geometries
zbMATH Open document ID: 0807.51011
DOI: 10.1016/0097-3165(94)90012-4
author: Frederick J. Fuglister
published in: Journal of Combinatorial Theory. Series A
publication date: 1994-08-09T00:00:00Z
review text: A generalized Moore geometry is an incidence structure with \(a + 1\) points on each line and \(b + 1\) lines through each point such that: Two distrinct points are incident with at most one line and if they are not incident then there is required a sequence of at most \(d\) consecutive lines that give a bridge between them. \(d\) is called the diameter of the geometry. To any two points that require a sequence of \(d\) lines there exist \(c\) distinct sequences of \(d\) lines connecting them. The sequence is unique if it is shorter than \(d\). [\textit{C. Roos} and \textit{A. J. van Zanten}, J. Comb. Theory B 33, 197-212 (1982; Zbl 0488.05055 )]. The author proved earlier that \(d \leq 13\). Now, here it is shown that for the case \(a = b\) the boundary can be reduced to 3 if the geometry is not trivial. The proof is done by investigating the characteristic equation of the intersection matrix and its eigenvalues. For this computer algebra programs are used.
Mathematics Subject Classification ID: 51E30
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 617600
zbMATH Keywords: diameter of a geometry
zbMATH Keywords: incidence matrix
zbMATH Keywords: Moore geometry
reviewed by: Herbert Hotje
MaRDI profile type: Publication
full work available at URL: 0097-3165(94)90012-4
OpenAlex ID: W2091857249
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description: scientific article; zbMATH DE number 617600