Axioms for infinite matroids
Henning Bruhn, Reinhard Diestel, Matthias Kriesell, Rudi Pendavingh,, Paul Wollan
TL;DR
This paper establishes axiomatic foundations for infinite matroids, including duality, using various structural concepts, thereby completing a longstanding mathematical problem posed by Rado in 1966.
Contribution
It provides a comprehensive axiomatic framework for non-finitary infinite matroids, resolving a problem posed by Rado in 1966.
Findings
Axioms for infinite matroids with duality are formulated.
The framework applies to non-finitary infinite matroids.
The solution completes Rado's 1966 problem.
Abstract
We give axiomatic foundations for non-finitary infinite matroids with duality, in terms of independent sets, bases, circuits, closure and rank. This completes the solution to a problem of Rado of 1966.
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Taxonomy
TopicsAdvanced Algebra and Logic · Advanced Graph Theory Research · Rough Sets and Fuzzy Logic