  Let X,Y be finite sets and T a set of functions from X -> Y which we will
call "tableaux". We define a simplicial complex whose facets, all of the same
dimension, correspond to these tableaux. Such "tableau complexes" have many
nice properties, and are frequently homeomorphic to balls, which we prove using
vertex decompositions.
  In our motivating example, the facets are labeled by semistandard Young
tableaux, and the more general interior faces are labeled by Buch's set-valued
semistandard tableaux. One vertex decomposition of this "Young tableau complex"
parallels Lascoux's transition formula for vexillary double Grothendieck
polynomials. Consequently, we obtain formulae (both old and new) for these
polynomials. In particular, we present a common generalization of the formulae
of Wachs and Buch, each of which implies the classical tableau formula for
Schur polynomials.
