I am looking for a (already-studied or interesting) class of Matroids such that - Class of Gammoids are contained in it
One example would be Strongly-base-orderable Matroids. I would also be grateful if someone knows a class of Matroids such that
- Class of Gammoids are contained in it AND
- It is contained in the class of "Strongly-base-orderable" Matroids.
By the way, strongly-base-orderable is a property such that : GIven any two bases I,J of the Matroid, there exists a bijection \pi between I-J and J-I such that given any subset H of I-J, I- H +\pi(H) and J - \pi(H) + H is a base in the Matroid. (In Oxley's "Matroid theory" pp410 )
Motivation : Well, I have something I can show for Gammoids but cannot for Strongly-base-orderable Matroids, although computational evidence suggests that it holds for general Matroids.