Completed
The Hopf monoid of graphs.
Class Central Classrooms beta
YouTube videos curated by Class Central.
Classroom Contents
Algebraic Structures on Polytopes
Automatically move to the next video in the Classroom when playback concludes
- 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.
