Séminaire Lotharingien de Combinatoire, B63f (2010), 17 pp.

Andrew Berget

Tableaux in the Whitney Module of a Matroid

Abstract. The Whitney module of a matroid is a natural analogue of the tensor algebra of the exterior algebra of a vector space that takes into account the dependencies of the matroid.

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.

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