For panhandle and Schubert matroids built from multiples of a group element, matchability to another such matroid is characterized by the target being uniform, with new sparse paving conditions alongside.
Crapo, Single-element extensions of matroids,Journal of research, National Bureau of Standards69B (1965), 55–66
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Matchings in matroids over abelian groups, II
For panhandle and Schubert matroids built from multiples of a group element, matchability to another such matroid is characterized by the target being uniform, with new sparse paving conditions alongside.