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Hopf Monoids and Generalized Permutahedra A. J. Angulo School Psychologist Bend-La Pine School

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School Psychologist Bend-La Pine School District

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Hopf Monoids and Generalized Permutahedra A. J. Angulo School Psychologist Bend-La Pine SchoolGeneralized permutahedra are polytopes that arise in combinatorics, algebraic geometry, representation theory, topology, and optimization. They possess a rich combinatorial structure. Out of this structure we build a Hopf monoid in the category of species. Species provide a unifying framework for organizing families of combinatorial objects. Many species carry a Hopf monoid structure and are related to generalized permutahedra by means of morphisms of

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