Výsledky vyhledávání - "Supina, Mariel"

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Algebra and Combinatorics of the Brion map on Generalized Permutahedra

The Brion morphism maps a generalized permutahedron to a collection of posets associated to its vertices. We compute this map explicitly for the Hopf monoids of permutahedra, associahedra, and orbit polytopes, and we explore the dual Brion map of the

Externí odkaz: http://arxiv.org/abs/2310.09900

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Techniques in equivariant Ehrhart theory

Autor: Elia, Sophia, Kim, Donghyun, Supina, Mariel

Equivariant Ehrhart theory generalizes the study of lattice point enumeration to also account for the symmetries of a polytope under a linear group action. We present a catalogue of techniques with applications in this field, including zonotopal deco

Externí odkaz: http://arxiv.org/abs/2205.05900

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The Universal Valuation of Coxeter Matroids

Autor: Eur, Christopher, Sanchez, Mario, Supina, Mariel

Coxeter matroids generalize matroids just as flag varieties of Lie groups generalize Grassmannians. Valuations of Coxeter matroids are functions that behave well with respect to subdivisions of a Coxeter matroid into smaller ones. We compute the univ

Externí odkaz: http://arxiv.org/abs/2008.01121

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The equivariant Ehrhart theory of the permutahedron

Autor: Ardila, Federico, Supina, Mariel, Vindas-Meléndez, Andrés R.

Equivariant Ehrhart theory enumerates the lattice points in a polytope with respect to a group action. Answering a question of Stapledon, we describe the equivariant Ehrhart theory of the permutahedron, and we prove his Effectiveness Conjecture in th

Externí odkaz: http://arxiv.org/abs/1911.11159

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The Hopf Monoid of Orbit Polytopes

Autor: Supina, Mariel

Publikováno v: Journal of Combinatorics 11 (2020) 575-601

Many families of combinatorial objects have a Hopf monoid structure. Aguiar and Ardila introduced the Hopf monoid of generalized permutahedra and showed that it contains various other notable combinatorial families as Hopf submonoids, including graph

Externí odkaz: http://arxiv.org/abs/1904.08437

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