A construction of infinite sets of intertwines for pairs of matroids

Abstract

An intertwine of a pair of matroids is a matroid such that it, but none of its proper minors, has minors that are isomorphic to each matroid in the pair. For pairs for which neither matroid can be obtained, up to isomorphism, from the other by taking free extensions, free coextensions, and minors, we construct a family of rank-k intertwines for each sufficiently large integer k. We also treat some properties of these intertwines.

11 pages

References in corpus (1)

• The Lattice of Cyclic Flats of a Matroid

Cited by in corpus (3)

• Characterizations of transversal and fundamental transversal matroids
• Sparse paving matroids, basis-exchange properties, and cyclic flats
• The natural matroid of an integer polymatroid