Combinatorial Atlas for Log-Concave Inequalities

Combinatorial Atlas for Log-Concave Inequalities

Fields Institute via YouTube Direct link

Intro

1 of 19

1 of 19

Intro

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Combinatorial Atlas for Log-Concave Inequalities

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  1. 1 Intro
  2. 2 Example: binomial coefficients
  3. 3 Example: permutations with k inversions
  4. 4 Matroids: Conditions
  5. 5 Mason's Conjecture (1972)
  6. 6 Solution to Mason (3)
  7. 7 Warmup: graphical matroids refinement
  8. 8 Refinement for different matroids
  9. 9 Matroid contraction
  10. 10 Parallel number
  11. 11 Refinement for Mason (3)
  12. 12 When is equality achieved?
  13. 13 Equality conditions
  14. 14 Atlas example: matroid (simplified)
  15. 15 Hyperbolic inequality
  16. 16 Irreducibility condition
  17. 17 Inheritance condition
  18. 18 Subdivergence condition
  19. 19 Bottom-to-top principle for hyperbolic inequalities

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