Dowling group geometries and the critical problem
type: Item
instance of: scholarly article
title: Dowling group geometries and the critical problem
zbMATH Open document ID: 0628.05018
DOI: 10.1016/0095-8956(89)90067-1
author: Geoff Whittle
published in: Journal of Combinatorial Theory. Series B
publication date: 1989-01-01T00:00:00Z
review text: This paper relates the critical problem of Crapo and Rota to Dowling group geometries. If A is a finite group, \(Q_ r(A)\) is the rank r Dowling group geometry over A and M is a rank r matroid embeddable as a minor of \(Q_ r(A)\), then it is shown that the critical exponent of M over A is well defined and is determined by an evaluation of the characteristic polynomial of M. Classes of tangential k-blocks obtained from Dowling group geometries are also displayed. A consequence of the theory is that for the first time all cases of Hadwiger's conjecture can be stated as critical problems.
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 4021158
zbMATH Keywords: critical problem
zbMATH Keywords: Dowling group geometries
zbMATH Keywords: matroid
MaRDI profile type: Publication
full work available at URL: 0095-8956(89)90067-1
OpenAlex ID: W2015959301
cites work: A Decomposition for Combinatorial Geometries
cites work: An Affine Representation for Transversal Geometries
cites work: Modular Constructions for Combinatorial Geometries
cites work: Q3737438
cites work: Q5619114
cites work: Q5685088
cites work: A class of geometric lattices based on finite groups
cites work: Q5675735
cites work: Varieties of Combinatorial Geometries
cites work: Q4133651
cites work: Modular elements of geometric lattices
cites work: Supersolvable lattices
cites work: On the algebraic theory of graph colorings
cites work: Tangential 1-blocks over GF(3)
cites work: Q4111952
cites work: On the critical exponent of transversal matroids
cites work: Modularity in tangential k-blocks
cites work: Quotients of Tangential k-Blocks
cites work: Signed graphs
cites work: Biased graphs. I: Bias, balance, and gains
cites work: Biased graphs. II: The three matroids
description: scientific article; zbMATH DE number 4021158