Representation of matroids
Massimiliano Lunelli, Antonio Laface
TL;DR
This paper establishes a precise criterion for determining when a matroid can be represented over an algebraically closed field, and introduces an algorithm based on Groebner Bases to decide representability.
Contribution
It provides a necessary and sufficient condition for matroid representability over algebraically closed fields and develops an algorithm to decide this property.
Findings
Criterion for matroid representability over algebraically closed fields
Algorithm based on Groebner Bases for testing representability
Decides representability efficiently for given matroids
Abstract
In this paper we give a necessary and sufficient criterion for representability of a matroid over an algebraic closed field. This leads to an algorithm, based on an extension of Groebner Bases, in order to decide if a given matroid is representable over such a field.
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Taxonomy
TopicsPolynomial and algebraic computation · Commutative Algebra and Its Applications · Advanced Graph Theory Research