Enumeration of 2-Polymatroids on up to Seven Elements

@article{Savitsky2014EnumerationO2,
  title={Enumeration of 2-Polymatroids on up to Seven Elements},
  author={Thomas J. Savitsky},
  journal={SIAM J. Discret. Math.},
  year={2014},
  volume={28},
  pages={1641-1650}
}
A theory of single-element extensions of integer polymatroids analogous to that of matroids is developed. We present an algorithm to generate a catalog of 2-polymatroids, up to isomorphism. When we implemented this algorithm on a computer, obtaining all 2-polymatroids on at most seven elements, we discovered the surprising fact that the number of 2-polymatroids on seven elements fails to be unimodal in rank. 

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