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The Upper Bound Theorems
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Classroom Contents
Isabella Novik - Face Numbers - The Upper Bound Side of the Story
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- 1 Intro
- 2 I. Basics on Polytopes
- 3 Motivation --- the Upper Bound Problem
- 4 Properties of cyclic polytopes
- 5 A digression: simplicial complexes and simplicials W
- 6 The Upper Bound Theorems
- 7 Comments
- 8 II. There are many more spheres than polytopes
- 9 What proportion of d-polytopes are li l-neighborly
- 10 Summary so far
- 11 III. Cs polytopes and cs spheres
- 12 The Upper Bound Problem for cs polytopes and sp.
- 13 How neighborly can a cs polytope be?
- 14 Cs-2-neighborliness of cs polytopes W
- 15 From non-neighborliness to f-numbers W
- 16 Does it exist?
- 17 It does exist!
- 18 Summary and Open problems
