Infinite trees of matroids
Nathan Bowler, Johannes Carmesin
TL;DR
This paper extends the theory of infinite matroids by allowing both the matroids at tree nodes and the representing fields to be infinite, broadening the scope of their structural analysis.
Contribution
It introduces a generalized construction of infinite trees of matroids where node matroids and fields are both infinite, expanding previous finite-based frameworks.
Findings
Established a new framework for infinite trees of matroids.
Demonstrated the applicability to broader classes of matroids.
Provided foundational results for future research in infinite matroid theory.
Abstract
We generalise the construction of infinite matroids from trees of matroids to allow the matroids at the nodes, as well as the field over which they are represented, to be infinite.
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Taxonomy
TopicsAdvanced Graph Theory Research · Advanced Topology and Set Theory