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MIT Combinatorics Seminar

Tableau Complexes

Ezra Miller, (University of Minnesota)

Wednesday, November 2, 2005   4:30 pm    Room 2-142

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 P-partitions 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 (vertex-decomposable, 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.