Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, November 24, 2009, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Andrea Francke

A simple proof of the upper bound theorem (student talk, 45 min.)

The Upper Bound Theorem, first proved by McMullen in the 1970's, is one of the most fundamental theorems about convex polytopes. The theorem gives exact upper bounds for the maximum number of faces of a d-dimensional convex polytope with n vertices. In this article, a new, simple proof is given that reduces the theorem to a purely combinatorial problem about systems of sets with certain intersection properties, and then uses methods from (multi)linear algebra to solve the latter. This paper is one of the clearest and most elegant applications of linear algebra methods in combinatorics.

Paper by Noga Alon and Gil Kalai: A simple proof of the upper bound theorem, European Journal of Combinatorics 6 (1985), 211-214.

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