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3.4. Generalized permutahedra: Posets, graphs, matroids
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Classroom Contents
Algebraic Structures on Polytopes
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- 1 Intro
- 2 What is combinatorics about? A personal view
- 3 11. A tale of two polytopes Permutations
- 4 1.2. A tale of two polytopes: Associations
- 5 13. Motivating application Inverting power series
- 6 Inverting power series: Multiplication
- 7 Inverting power series Composition
- 8 21. Hopf monoids: Definition
- 9 The Hopf monoid of graphs.
- 10 The Hopf monoid of posets
- 11 The Hopf monoid of matroids
- 12 22. The antipode of a Hopf moncid
- 13 Examples: The antipode of a graph, matroid, poset
- 14 Generalized permutahedra in 3-D
- 15 3.3. The Hopf monoid GP Coproduct
- 16 The Hopf monoid of generalized permutahedra.
- 17 3.4. Generalized permutahedra: Posets, graphs, matroids
- 18 3.5. The antipode of GP
- 19 The antipodes of graphs, matroids, posets
- 20 Many antipode formulas
- 21 Characters of Hopf monoids.
- 22 The group of characters for permutahedra
- 23 The group of characters of associahedra
- 24 6.1. Current direction 1: the polytope algebra.
