Maximal unimodular systems of vectors
type: Item
instance of: scholarly article
title: Maximal unimodular systems of vectors
zbMATH Open document ID: 0933.15004
author: Viacheslav Grishukhin
author: Vladimir I. Danilov
published in: European Journal of Combinatorics
publication date: 1999-12-02T00:00:00Z
review text: Assertions of \textit{P. D. Seymour} [J. Comb. Theory, Ser. B 28, 305-359 (1980; Zbl 0443.05027)] on unimodular systems of vectors (or \(U\)-systems) are refined and applied to maximal \(U\)-systems. A maximal \(U\)-system can be obtained as amalgams of simplest components. Three types of components exist: the root systems \(A_n\), the cographic systems of non-planar 3-connected cubic graphs, and the systems \(E_5\) representing the matroid \(R_{10}\). Necessary and sufficient conditions are derived for maximality of an amalgamated \(U\)-system. All 11 maximal \(U\)-systems of dimension 6 are described.
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 1348194
zbMATH Keywords: maximal \(U\)-systems
zbMATH Keywords: unimodular systems of vectors
zbMATH Keywords: root systems
zbMATH Keywords: cographic systems
zbMATH Keywords: cubic graphs
zbMATH Keywords: matroid
MaRDI profile type: Publication
full work available at URL: eujc.1999.0298
OpenAlex ID: W2021622607
cites work: Modular Constructions for Combinatorial Geometries
cites work: Discrete convexity and unimodularity. I.
cites work: On lattice dicing
cites work: Q5634104
cites work: Q3818127
cites work: Decomposition of regular matroids
DOI: 10.1006/EUJC.1999.0298
description: scientific article; zbMATH DE number 1348194