 
Summary: arXiv:math.CO/0209354v125Sep2002
The Catalan matroid.
Federico Ardila
fardila@math.mit.edu
September 4, 2002
Abstract
We show how the set of Dyck paths of length 2n naturally gives rise
to a matroid, which we call the "Catalan matroid" Cn. We describe
this matroid in detail; among several other results, we show that Cn
is selfdual, it is representable over Q but not over finite fields Fq 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 al
most simultaneously in the work of Klivans, who showed that they
are precisely the matroids whose independence complex is a shifted
complex.
1 Introduction
A Dyck path of length 2n is a path in the plane from (0, 0) to (2n, 0), with
steps (1, 1) and (1, 1), that never passes below the xaxis. It is a classical
result (see for example [8, Corollary 6.2.3.(iv)]) that the number of Dyck
