Hopf Monoids and Generalized Permutahedra
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A01=Federico Ardila
A01=Marcelo Aguiar
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Author_Federico Ardila
Author_Marcelo Aguiar
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Product details
- ISBN 9781470467081
- Dimensions: 178 x 254mm
- Publication Date: 30 Sep 2023
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
- Language: English
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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. 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.
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.
Federico Ardila, San Francisco State University, California, and Universidad de Los Andes, Bogota, Colombia.
