MIT Combinatorics Seminar
Tableau Complexes
Ezra Miller, (University of Minnesota)
Wednesday, November 2, 2005 4:30 pm Room 2142
ABSTRACT

Consider a poset P with its elements labeled by
integers. For example, Young tableaux arise this way
when P is a Young diagram, and Ppartitions arise
for more general posets P. In joint work with Allen Knutson and Alex
Yong we define, for any finite set of
labelings of P, a simplicial complex whose
facets correspond to these labelings and whose smaller
faces are labelings of P with sets of integers. Under
interesting conditions, these \emph{tableau complexes}
are (vertexdecomposable, and hence shellable) balls or
spheres, and their interior faces are easily identified.
Explicit Hilbert series formulas result. The special
case where the facets are semistandard Young tableaux
yields formulas for polynomials arising in Schubert
Calculus.


