Grassmann-Plücker relations and matroids with coefficients
type: Item
instance of: scholarly article
title: Grassmann-Plücker relations and matroids with coefficients
zbMATH Open document ID: 0748.05040
DOI: 10.1016/0001-8708(91)90036-7
author: Walter Wenzel
author: Andreas W. M. Dress
published in: Advances in Mathematics
publication date: 1992-06-25T00:00:00Z
review text: Using the concept of fuzzy rings, this paper presents a conceptual framework which allows a unified treatment of the algebraic and the combinatorial aspects of the Grassmann-Plücker identities which have played an important role in invariant and syzygy theory and in combinatorics. It has been shown that a matroid with coefficients of finite rank can also be defined in terms of its associated Grassmann- Plücker map, which in a way generalizes classical determinants. More precisely, it has been shown that such matroids correspond naturally and in a one-to-one fashion to equivalence classes of appropriately defined Grassmann-Plücker maps.
reviewed by: Bai Kishan Dass
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 10168
zbMATH Keywords: matroids
zbMATH Keywords: fuzzy ring
zbMATH Keywords: Grassmann-Plücker identities
zbMATH Keywords: Grassmann-Plücker maps
MaRDI profile type: Publication
full work available at URL: 0001-8708(91)90036-7
OpenAlex ID: W1980749407
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description: scientific article; zbMATH DE number 10168