This project finds and counts transversal matroids and is part of my Master's thesis (link not available yet) Extensions of transversal matroids for the Master in Advanced Mathematics and Mathematical Engineering at UPC (Barcelona).
The code is written entirely in SageMath, although most of the tools are Python native. The strategy that we follow is described in the referenced project.
File minimal_presentations.txt contains one minimal presentation of a transversal matroid in each line. File maximal_presentations.txt contains one maximal presentation of a (distinct) transversal matroid in each line.
In these files, each line is of the form n [{...}, {...}, ...] where n is the size of the ground set and, between brackets, are the sets of the presentation.
Example: 5 [{1, 4, 5}, {2, 4, 5}, {3, 4}]