The minors of matroids with an adjoint

Abstract

If $M$ is a matroid, then a simple matroid $M^{\prime }$ with the same rank as $M$ is an adjoint of $M$ if there is an inclusion-reversing embedding $\varphi$ of the lattice of flats of $M$ into the lattice of flats of $M^{\prime }$ such that $\varphi$ maps the hyperplanes of $M$ bijectively onto the points of $M^{\prime }$. In this note, we provide a proof that the class of matroids with an adjoint is minor-closed.

Version 2 makes some minor corrections and adds some explanatory material. 4 pages