Discrete CATS Seminar

Monday, October 31, 2016

2PM, POT 745

Speaker: Federico Ardila, San Francisco State University

Title: The algebraic and combinatorial structure of generalized permutahedra

Abstract: Generalized permutahedra are a beautiful family of polytopes which are known to have a rich combinatorial structure. We explore the Hopf algebraic structure of this family, and use it to unify old results, prove new results, and answer open questions about families of interest such as graphs, matroids, posets, trees, set partitions, hypergraphs, and simplicial complexes. As a corollary, we obtain a new polyhedral approach for computing the multiplicative and compositional inverses of a power series.  The talk is based on joint work with Marcelo Aguiar, and will assume no previous knowledge of Hopf algebras or generalized permutahedra.