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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Bibliographic Details
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
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ISSN0012-365X
1872-681X
DOI10.1016/j.disc.2009.04.007

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Summary: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.
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ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2009.04.007