Amalgams of extremal matroids with no -minor

For an integer ℓ ≥ 2 , let U ( ℓ ) be the class of matroids with no U 2 , ℓ + 2 -minor. A matroid in U ( ℓ ) is extremal if it is simple and has no simple rank-preserving single-element extension in U ( ℓ ) . An amalgam of two matroids is a simultaneous extension of both on the union of the two ground sets. We study amalgams of extremal matroids in U ( ℓ ) : we determine which amalgams are in U ( ℓ ) and which are extremal in U ( ℓ ) .