Tag Archives: upper bound theorem

Richard Stanley: How the Proof of the Upper Bound Theorem (for spheres) was Found

The upper bound theorem asserts that among all d-dimensional polytopes with n vertices, the cyclic polytope maximizes the number of facets (and k-faces for every k). It was proved by McMullen for polytopes in 1970, and by Stanley for general triangulations … Continue reading

Posted in Combinatorics, Convex polytopes | Tagged , | 2 Comments

How the g-Conjecture Came About

Update: Slides from a great 2014 lecture on the g-conjecture by Lou Billera in the conference celebrating Richard Stanley’s 70th birthday. This post complements Eran Nevo’s first  post on the -conjecture 1) Euler’s theorem Euler Euler’s famous formula for the … Continue reading

Posted in Combinatorics, Convex polytopes, Open problems | Tagged , , , , | 9 Comments