Im currently reading Matroids: A geometric introduction by Gordon and McNulty. I understand that two non-isomorphic polynomials can have the same tutte-polynomial, but is there a way to be able to identify the characteristics that such matroids have and be able to group them together?
So far I know that they must have the same number of elements,
and the two matroids should be identical if I contract/delete both through a chosen element.
How else would I be able to create such matroids?