Geometric algebra for combinatorial geometries
type: Item
instance of: scholarly article
title: Geometric algebra for combinatorial geometries
zbMATH Open document ID: 0684.05013
DOI: 10.1016/0001-8708(89)90013-3
author: Walter Wenzel
author: Andreas W. M. Dress
published in: Advances in Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The starting point of this paper is a correspondence in which with a given combinatorial geometry, or matroid, M defined on a finite set E a certain abelian group \(\Pi_ m\) is associated in a canonical fashion. This group is called the Tutte-group of M, and the study of its structure is the main purpose of the paper. Particularly the following two problems are discussed. First, there is a group of theorems describing how \(\Pi_ M\) can be defined in terms of generators and relations in many possible ways using either the basis of M or its hyperplanes or its circuits etc. Second, another group of theorems explains how \(\Pi_ M\) controls the representability of M as well as its properties like regularity, binarity, ternarity, orientability etc., and how it relates to the universal representation ring of M. Other more detailed results concerning the structure of Tutte-groups can be found in three forthcoming papers briefly characterized in the text, this paper is announced to be the first and introductory in the series of papers.
reviewed by: J.Libicher
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 4120185
zbMATH Keywords: combinatorial geometry
zbMATH Keywords: matroid
zbMATH Keywords: abelian group
zbMATH Keywords: Tutte-group
MaRDI profile type: Publication
full work available at URL: 0001-8708(89)90013-3
OpenAlex ID: W2086795154
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description: scientific article; zbMATH DE number 4120185