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# 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} }

- Published 2003 in J. Comb. Theory, Ser. A
DOI:10.1016/S0097-3165(03)00121-3

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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