The Catalan matroid

@article{Ardila2003TheCM,
  title={The Catalan matroid},
  author={Federico Ardila},
  journal={J. Comb. Theory, Ser. A},
  year={2003},
  volume={104},
  pages={49-62}
}
We show how the set of Dyck paths of length 2n naturally gives rise to a matroid, which we call the " Catalan matroid " C n. We describe this matroid in detail; among several other results, we show that C n is self-dual, it is representable over Q but not over finite fields F q with q ≤ n − 2, and it has a nice Tutte polynomial. We then generalize our construction to obtain a family of matroids, which we call " shifted matroids ". They arose independently and almost simultaneously in the work… CONTINUE READING

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