Mathematics Colloquia and Seminars

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One of the most fundamental invariants of a simplicial complex is its f-vector, which lists the number of faces the complex has in each dimension. One of the central challenges of geometric combinatorics is that of characterizing the set of f-vectors for interesting classes of complexes. A characterization of the f-vectors of Cohen-Macaulay complexes was given by Stanley; this result was refined to a characterization of the f-vectors of a-balanced Cohen-Macaulay complexes (Bjorner, Frankl, and Stanley) and a later to a characterization of the f-vectors of Cohen-Macaulay subcomplexes of joins of boundaries of simplices (B., Novik). This talk will present a common generalization of these latter two results (B., Novik), and explore some of the tools used.