Extensions of transversal valuated matroids
Alex Fink, Jorge Alberto Olarte
TL;DR
This paper investigates single-element extensions of transversal valuated matroids, demonstrating that tropical presentations with minimal finite entries share key properties with minimal non-valuated transversal presentations, building on prior work.
Contribution
It introduces new properties of tropical presentations of valuated matroids with minimal finite entries, extending previous results to the valuated case.
Findings
Tropical presentations with minimal finite entries have properties similar to non-valuated cases.
Extensions of transversal valuated matroids can be characterized via tropical presentations.
The work generalizes known properties to the valuated matroid setting.
Abstract
Following up on our previous work, we study single-element extensions of transversal valuated matroids. We show that tropical presentations of valuated matroids with a minimal set of finite entries enjoy counterparts of the properties proved by Bonin and de Mier of minimal non-valuated transversal presentations.
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Taxonomy
TopicsAdvanced Graph Theory Research · Advanced Algebra and Logic · graph theory and CDMA systems