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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Vydáno v:	Discrete mathematics Ročník 271; číslo 1; s. 71 - 100
Hlavní autoři:	Govaert, E., Van Maldeghem, H.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier B.V 28.09.2003 Elsevier
Témata:	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
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Popis
Shrnutí:	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