In this paper we indicate the role that tableaux can play in
describing the Whitney module. We will use our results to describe a
basis of the Whitney module of a certain class of matroids known as
freedom (also known as Schubert, or shifted) matroids. The doubly
multilinear submodule of the Whitney module is a representation of
the symmetric group. We will describe a formula for the multiplicity
hook shapes in this representation in terms of the no broken circuit
sets.

Received: February 8, 2010. Accepted: June 15, 2010.

The following versions are available:

- PDF (258 K)
- PostScript (459 K)
- DVI version
- Tex version