Linear sets in finite projective spaces

In this paper linear sets of finite projective spaces are studied and the “dual” of a linear set is introduced. Also, some applications of the theory of linear sets are investigated: blocking sets in Desarguesian planes, maximum scattered linear sets, translation ovoids of the Cayley Hexagon, transl...

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Published inDiscrete mathematics Vol. 310; no. 22; pp. 3096 - 3107
Main Author Polverino, Olga
Format Journal Article Conference Proceeding
LanguageEnglish
Published Kidlington Elsevier B.V 28.11.2010
Elsevier
Subjects
Algebra
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Finite field
Functional analysis
Geometry
Hexagons
Mathematical analysis
Mathematics
Number theory
Planes
Projective space
Sciences and techniques of general use
Subgeometry
Translations
Finite field
Subgeometry
Projective space
Maximum
Translation
Linear theory
Blocking
Discrete mathematics
Set theory
Orthogonal space
Combinatorics
Linear space
Online AccessGet full text
ISSN0012-365X
1872-681X
DOI10.1016/j.disc.2009.04.007

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Abstract In this paper linear sets of finite projective spaces are studied and the “dual” of a linear set is introduced. Also, some applications of the theory of linear sets are investigated: blocking sets in Desarguesian planes, maximum scattered linear sets, translation ovoids of the Cayley Hexagon, translation ovoids of orthogonal polar spaces and finite semifields. Besides “old” results, new ones are proven and some open questions are discussed.
AbstractList In this paper linear sets of finite projective spaces are studied and the "dual" of a linear set is introduced. Also, some applications of the theory of linear sets are investigated: blocking sets in Desarguesian planes, maximum scattered linear sets, translation ovoids of the Cayley Hexagon, translation ovoids of orthogonal polar spaces and finite semifields. Besides "old" results, new ones are proven and some open questions are discussed.
Author Polverino, Olga
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  surname: Polverino
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  email: olga.polverino@unina2.it, opolveri@unina.it
  organization: Seconda Università degli Studi di Napoli, Dipartimento di Matematica, via Vivaldi 43, I-81100 Caserta, Italy
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Issue 22
Keywords Finite field
Subgeometry
Projective space
Maximum
Translation
Linear theory
Blocking
Discrete mathematics
Set theory
Orthogonal space
Combinatorics
Linear space
Language English
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Snippet In this paper linear sets of finite projective spaces are studied and the “dual” of a linear set is introduced. Also, some applications of the theory of linear...
In this paper linear sets of finite projective spaces are studied and the "dual" of a linear set is introduced. Also, some applications of the theory of linear...
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SubjectTerms Algebra
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Finite field
Functional analysis
Geometry
Hexagons
Mathematical analysis
Mathematics
Number theory
Planes
Projective space
Sciences and techniques of general use
Subgeometry
Translations
Title Linear sets in finite projective spaces
URI https://dx.doi.org/10.1016/j.disc.2009.04.007
https://www.proquest.com/docview/1671226638
Volume 310
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