Embedding Finite Partial Linear Spaces in Finite Translation Nets

. In the 1970’s Paul Erdős and Dominic Welsh independently posed the problem of whether all finite partial linear spaces are embeddable in finite projective planes. Except for the case when has a unique embedding in a projective plane with few additional points, very little has been done which is di...

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Bibliographic Details
Published in:Journal of geometry 2009, Vol.91 (1-2), p.73-83
Main Authors: Moorhouse, G. Eric, Williford, Jason
Format: Article
Language:English
Subjects:
Geometry
Mathematics
Mathematics and Statistics
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Summary:. In the 1970’s Paul Erdős and Dominic Welsh independently posed the problem of whether all finite partial linear spaces are embeddable in finite projective planes. Except for the case when has a unique embedding in a projective plane with few additional points, very little has been done which is directly applicable to this problem. In this paper it is proved that every finite partial linear space is embeddable in a finite translation net generated by a partial spread of a vector space of even dimension. The question of whether every finite partial linear space is embedded in a finite André net is also explored. It is shown that for each positive integer n there exist finite partial linear spaces which do not embed in any André net of dimension less than or equal to n over its kernel.
ISSN:0047-2468
1420-8997
DOI:10.1007/s00022-008-2066-4