Cameron-Liebler $k$-classes in \(\mathrm{PG}(2k+1,q)\)
type: Item
instance of: scholarly article
title: Cameron-Liebler $k$-classes in \(\mathrm{PG}(2k+1,q)\)
zbMATH Open document ID: 1424.51005
author: Morgan Rodgers
author: Andries Vansweevelt
author: Leo Storme
published in: Combinatorica
publication date: 2019-02-01T00:00:00Z
review text: Let $A$ be the point line incidence matrix of \(\mathrm{PG}(n,q)\), then a set of lines \(L\) is a Cameron-Liebler line class if the characteristic function \(\chi_L\) belongs to \(\mathrm{row}(A)\). The authors generalize this definition to the following. A set of \(k\)-spaces in \(P(n,q)\) is a Cameron-Liebler \(k\)-class if the characteristic function \(\chi_L\) belongs to \(\mathrm{row}(A_k)\), where \(A_k\) is the points \(k\)-spaces incidence matrix of \(\mathrm{PG}(n,q)\). The authors give many results about Cameron-Liebler \(k\) classes analogous to results about Cameron-Liebler line classes. Further, they give a connection to \(k\)-spreads which parallels the situation for line classes in \(\mathrm{PG}(3,q)\). Additionally, they give connections to other geometric objects and Erdős-Ko-Rado sets, proving some results about the existence of these objects.
reviewed by: Steven T. Dougherty
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 05E30
zbMATH DE Number: 7011201
zbMATH Keywords: Cameron-Liebler line classes
zbMATH Keywords: $k$-spreads
zbMATH Keywords: Erdős-Ko-Rado sets
zbMATH Keywords: projective geometry
describes a project that uses: Gurobi
MaRDI profile type: Publication
full work available at URL: s00493-016-3482-y
OpenAlex ID: W2601283133
DOI: 10.1007/S00493-016-3482-Y
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description: scientific article; zbMATH DE number 7011201