Forgetful polygons as generalizations of semi-affine planes

We generalize the notion of a semi-affine plane to structures with higher girth n. We prove that, in the finite case, for n odd, and with an additional assumption also for n even, these geometries, which we call forgetful n-gons, always arise from (finite) generalized n-gons by ‘forgetting’ lines....

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Bibliographic Details
Published in:Discrete mathematics Vol. 271; no. 1; pp. 71 - 100
Main Authors: Govaert, E., Van Maldeghem, H.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 28.09.2003
Elsevier
Subjects:
Exact sciences and technology
Finite generalized quadrangles
Generalized polygon
Geometry
Mathematics
Sciences and techniques of general use
Semi-affine plane
Semiplane
51E12
Semiplane
Finite generalized quadrangles
Generalized polygon
Semi-affine plane
Geometry
Projective plane
Affine plane
Classification
Affine geometry
Semi affine plane
Projective geometry
ISSN:0012-365X, 1872-681X
Online Access:Get full text
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Summary:We generalize the notion of a semi-affine plane to structures with higher girth n. We prove that, in the finite case, for n odd, and with an additional assumption also for n even, these geometries, which we call forgetful n-gons, always arise from (finite) generalized n-gons by ‘forgetting’ lines.
ISSN:0012-365X
1872-681X
DOI:10.1016/S0012-365X(02)00871-3