On classification of some finite linear spaces

On classification of some finite linear spaces

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We classified all finite linear spaces having property: for every pair L, L' of intersecting lines, and every point p not on either of these, there are L lines through p disjoint from both L and L', where the nonnegative number L is constant. This space will be denoted by (2i,0,L)-interlac...

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Bibliographic Details
Main Author: Ibrahim Gunaltılı
Format: Article
Language:English
Published: BİSKA Bilisim Company 2015-11-01
Series:New Trends in Mathematical Sciences
Subjects:
Linear space
interlaced space
projective plane
affine plane
semiaffine linear space.
Online Access:https://ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=3096
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spelling doaj-2b94e655c6594b7e80f4d7188f49a87a2020-11-25T00:20:50ZengBİSKA Bilisim CompanyNew Trends in Mathematical Sciences2147-55202147-55202015-11-01341041133096On classification of some finite linear spacesIbrahim Gunaltılı0Dr.We classified all finite linear spaces having property: for every pair L, L' of intersecting lines, and every point p not on either of these, there are L lines through p disjoint from both L and L', where the nonnegative number L is constant. This space will be denoted by (2i,0,L)-interlaced. In the present paper, we will show that this property (with L arbitrary) essentially characterizes the semia¢ ne planes with non-constant line size. For linear spaces with constant line size, this property does not seem to be strong enough, but we derive some necessary conditions on the parameters showing that examples will be hard to find.https://ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=3096Linear spaceinterlaced spaceprojective planeaffine planesemiaffine linear space.
collection DOAJ
language English
format Article
sources DOAJ
author Ibrahim Gunaltılı
spellingShingle Ibrahim Gunaltılı
On classification of some finite linear spaces
New Trends in Mathematical Sciences
Linear space
interlaced space
projective plane
affine plane
semiaffine linear space.
author_facet Ibrahim Gunaltılı
author_sort Ibrahim Gunaltılı
title On classification of some finite linear spaces
title_short On classification of some finite linear spaces
title_full On classification of some finite linear spaces
title_fullStr On classification of some finite linear spaces
title_full_unstemmed On classification of some finite linear spaces
title_sort on classification of some finite linear spaces
publisher BİSKA Bilisim Company
series New Trends in Mathematical Sciences
issn 2147-5520
2147-5520
publishDate 2015-11-01
description We classified all finite linear spaces having property: for every pair L, L' of intersecting lines, and every point p not on either of these, there are L lines through p disjoint from both L and L', where the nonnegative number L is constant. This space will be denoted by (2i,0,L)-interlaced. In the present paper, we will show that this property (with L arbitrary) essentially characterizes the semia¢ ne planes with non-constant line size. For linear spaces with constant line size, this property does not seem to be strong enough, but we derive some necessary conditions on the parameters showing that examples will be hard to find.
topic Linear space
interlaced space
projective plane
affine plane
semiaffine linear space.
url https://ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=3096
work_keys_str_mv AT ibrahimgunaltılı onclassificationofsomefinitelinearspaces
_version_ 1725365513727508480

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