Algebraic Structures on Polytopes

Algebraic Structures on Polytopes

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Intro

1 of 24

1 of 24

Intro

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Algebraic Structures on Polytopes

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

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