Algebraic characteristic sets of matroids
type: Item
instance of: scholarly article
title: Algebraic characteristic sets of matroids
zbMATH Open document ID: 0589.05025
DOI: 10.1016/0095-8956(88)90096-2
author: Gary Gordon
published in: Journal of Combinatorial Theory. Series B
publication date: 1988-01-01T00:00:00Z
review text: For a matroid M, define the algebraic characteristic set \(\chi_ A(M)\) to be the set of field characteristics over which M can be algebraically represented. We construct many examples of rank three matroids with finite, non-singleton algebraic characteristic sets. We also determine \(\chi_ A(PG(2,p))\) and \(\chi_ A(AG(2,p))\). An infinite family of rank matroids with empty algebraic characteristic set is constructed. In addition, we answer some antichain and excluded minor questions for algebraic representability over a given field F.
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 3946152
zbMATH Keywords: matroid
zbMATH Keywords: algebraic characteristic set
MaRDI profile type: Publication
full work available at URL: 0095-8956(88)90096-2
OpenAlex ID: W2120177358
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description: scientific article; zbMATH DE number 3946152