The minors of matroids with an adjoint
Kevin Grace

TL;DR
This paper proves that the class of matroids possessing an adjoint, a related simple matroid with a specific lattice embedding, remains closed under taking minors, highlighting structural stability within this class.
Contribution
It establishes that the class of matroids with an adjoint is minor-closed, providing a key structural property for this class of matroids.
Findings
The class of matroids with an adjoint is minor-closed.
Provides a proof of minor-closure for this class.
Highlights structural stability of matroids with an adjoint.
Abstract
If is a matroid, then a simple matroid with the same rank as is an adjoint of if there is an inclusion-reversing embedding of the lattice of flats of into the lattice of flats of such that maps the hyperplanes of bijectively onto the points of . In this note, we provide a proof that the class of matroids with an adjoint is minor-closed.
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Taxonomy
TopicsAdvanced Algebra and Logic · Fuzzy and Soft Set Theory
