On k-sets of class \([0,q/2-1,q/2,q/2+1,q]\) in a plane of even order q
type: Item
instance of: scholarly article
title: On k-sets of class \([0,q/2-1,q/2,q/2+1,q]\) in a plane of even order q
zbMATH Open document ID: 0586.51010
DOI: 10.1016/S0195-6698(85)80044-5
published in: European Journal of Combinatorics
publication date: 1985-01-01T00:00:00Z
review text: A set K of k points in a projective plane is said to be of class \([m_ 1,m_ 2,...,m_ s],\) \(0\leq m_ 1<m_ 2<...<m_ s\leq q+1\) (where q is the order of the plane) if for each line \(\ell\) of the plane, \(| K\cap \ell |\) is one of the numbers \(m_ i.\) The paper is a bit more general than the title indicates. All k-sets of type \((m_ 1,m_ 2)\) are listed; much information is given on k-sets of type \([m_ 1,m_ 2,m_ 3]\) and \([m_ 1,m_ 2,m_ 3,m_ 4]\). The final result is that when \(q\geq 8\) there is no set of the type indicated in the title with a unique O-secant. The point sets which show up are such things as affine planes, dual affine planes, ovals, dual ovals or one of the above with a few points added or deleted.
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 3940119
zbMATH Keywords: k-arc
zbMATH Keywords: projective plane
zbMATH Keywords: k-sets
zbMATH Keywords: dual ovals
author: M. J. de Resmini
reviewed by: Theodore G. Ostrom
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3940119