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Linear spaces with line range {n−1, n, n + 1} and at most n2 points

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

Lynn Margaret Batten
Lynn Margaret Batten
Affiliation:
Département de Mathématique, Université Libre de Bruxelles, C. P. 216 —Campus Plaine, Boulevard du Triomph, B-1050 Bruxelles, Belgique
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Abstract

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We characterize all finite linear spaces with p ≤ n2 points where n ≥ 8 for p ≠ n2 − 1 and n ≥ 23 for p = n2−1, and the line range is {n−1, n, n+1}. All such linear spaces are shown to be embeddable in finite projective planes of order a function of n. We also describe the exceptional linear spaces arising from p < n2−1 and n ≥ 4.

MSC classification

Secondary: 05B25: Finite geometries
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 2 , December 1980 , pp. 215 - 228
Copyright
Copyright © Australian Mathematical Society 1980

References

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