Blocking sets of small size and colouring in finite affine planes

Blocking sets of small size and colouring in finite affine planes

Let<em> (S, L) </em>be an either linear or semilinear space and<em> X ⊂ S</em>. Starting from <em>X</em> we define three types of colourings of the points of <em>S</em>. We characterize the Steiner systems<em> S(2, k, ν)</em> which have a c...

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Main Authors: Sandro Rajola, Maria Scafati Tallini
Format: Article
Language:English
Published: Università degli Studi di Catania 1997-11-01
Series:Le Matematiche
Online Access:http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/420
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spelling doaj-f9c2f89a5d9b4cf4a4e5ba7ebac213572020-11-25T03:09:19ZengUniversità degli Studi di CataniaLe Matematiche0373-35052037-52981997-11-01522417429392Blocking sets of small size and colouring in finite affine planesSandro RajolaMaria Scafati TalliniLet<em> (S, L) </em>be an either linear or semilinear space and<em> X ⊂ S</em>. Starting from <em>X</em> we define three types of colourings of the points of <em>S</em>. We characterize the Steiner systems<em> S(2, k, ν)</em> which have a colouring of the first type with <em>X = {P}</em>. By means of such colourings we construct blocking sets of small size in affine planes of order <em>q</em>. In particular, from the second and third type of colourings we get blocking sets<em> B</em> with<em> |B| ≤ 2q − 2.</em><br />http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/420
collection DOAJ
language English
format Article
sources DOAJ
author Sandro Rajola
Maria Scafati Tallini
spellingShingle Sandro Rajola
Maria Scafati Tallini
Blocking sets of small size and colouring in finite affine planes
Le Matematiche
author_facet Sandro Rajola
Maria Scafati Tallini
author_sort Sandro Rajola
title Blocking sets of small size and colouring in finite affine planes
title_short Blocking sets of small size and colouring in finite affine planes
title_full Blocking sets of small size and colouring in finite affine planes
title_fullStr Blocking sets of small size and colouring in finite affine planes
title_full_unstemmed Blocking sets of small size and colouring in finite affine planes
title_sort blocking sets of small size and colouring in finite affine planes
publisher Università degli Studi di Catania
series Le Matematiche
issn 0373-3505
2037-5298
publishDate 1997-11-01
description Let<em> (S, L) </em>be an either linear or semilinear space and<em> X ⊂ S</em>. Starting from <em>X</em> we define three types of colourings of the points of <em>S</em>. We characterize the Steiner systems<em> S(2, k, ν)</em> which have a colouring of the first type with <em>X = {P}</em>. By means of such colourings we construct blocking sets of small size in affine planes of order <em>q</em>. In particular, from the second and third type of colourings we get blocking sets<em> B</em> with<em> |B| ≤ 2q − 2.</em><br />
url http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/420
work_keys_str_mv AT sandrorajola blockingsetsofsmallsizeandcolouringinfiniteaffineplanes
AT mariascafatitallini blockingsetsofsmallsizeandcolouringinfiniteaffineplanes
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