Enumerating bases of self-dual matroids

@article{Maxwell2009EnumeratingBO,
  title={Enumerating bases of self-dual matroids},
  author={Molly Maxwell},
  journal={J. Comb. Theory, Ser. A},
  year={2009},
  volume={116},
  pages={351-378}
}
We define involutively self-dual matroids and prove a relationship between the bases and selfdual bases of these matroids. We use this relationship to prove an enumeration formula for the higher dimensional spanning trees in a class of cell complexes. This gives a new proof of Tutte’s theorem that the number of spanning trees of a central reflex is a perfect square and solves a problem posed by Kalai about higher dimensional spanning trees in simplicial complexes. We also give a weighted… CONTINUE READING
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