Hopf Monoids and Generalized Permutahedra
Seiten
2023
American Mathematical Society (Verlag)
978-1-4704-6708-1 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-6708-1 (ISBN)
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Generalized permutahedra are polytopes that arise in combinatorics, algebraic geometry, representation theory, topology, and optimization. They possess a rich combinatorial structure, from which we build a Hopf monoid in the category of species. We employ this structure to define and study polynomial invariants of various combinatorial structures.
Generalized 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 Hopf monoids. This includes the species of graphs, matroids, posets, set partitions, linear graphs, hypergraphs, simplicial complexes, and building sets, among others. We employ this algebraic structure to define and study polynomial invariants of the various combinatorial structures.
Generalized 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 Hopf monoids. This includes the species of graphs, matroids, posets, set partitions, linear graphs, hypergraphs, simplicial complexes, and building sets, among others. We employ this algebraic structure to define and study polynomial invariants of the various combinatorial structures.
Marcelo Aguiar, Cornell University, Ithaca, New York. Federico Ardila, San Francisco State University, California, and Universidad de Los Andes, Bogota, Colombia.
Erscheinungsdatum | 14.11.2023 |
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Reihe/Serie | Memoirs of the American Mathematical Society |
Verlagsort | Providence |
Sprache | englisch |
Maße | 178 x 254 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
Mathematik / Informatik ► Mathematik ► Graphentheorie | |
ISBN-10 | 1-4704-6708-9 / 1470467089 |
ISBN-13 | 978-1-4704-6708-1 / 9781470467081 |
Zustand | Neuware |
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