✦ LIBER ✦

Strongly Regular (α, β)-Geometries

✍ Scribed by Nicholas Hamilton; Rudolf Mathon

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 217 KB
Volume: 95
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.2000.3164

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✦ Synopsis

In this paper we introduce strongly regular (:, ;)-geometries. These are a class of geometries that generalise semipartial geometries. Like semipartial geometries the underlying point graph is strongly regular and this is part of the motivation for studying the geometries. In the paper several necessary conditions for existence are given. Strongly regular (:, ;)-reguli are defined, and it is shown how they may be used to construct strongly regular (:, ;)-geometries. This generalises similar results by J. A. Thas in (1980, European J. Combin. 1, 189 192) constructing semipartial geometries. Several constructions of strongly regular (:, ;)-geometries are given, and possible parameters of existence for small cases are listed.

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