Tags » Hirsch Conjecture

Karim Adiprasito: Flag simplicial complexes and the non-revisiting path conjecture

This post is authored by Karim Adiprasito

The past months have seen some exciting progress on diameter bounds for polytopes and polytopal complexes, both in the negative and in the positive direction.   1,378 more words

Convex Polytopes

Even if P=NP we might see no benefit

Inspired by an article in the New Scientist I am returning to a favourite subject – whether P = NP and what the implications would be in the (unlikely) case that this were so. 749 more words

Polymath3 (PHC6): The Polynomial Hirsch Conjecture - A Topological Approach

This is a new polymath3 research thread. Our aim is to tackle the polynomial Hirsch conjecture which asserts that there is a polynomial upper bound for the diameter of graphs of -dimensional polytopes with facets. 702 more words

Convex Polytopes

Polynomial Hirsch Conjecture 5: Abstractions and Counterexamples.

This is the 5th research thread of polymath3 studying the polynomial Hirsch conjecture. As you may remember, we are mainly interested in an abstract form of the problem about families of sets. 1,179 more words

Open Problems

Polymath3: Polynomial Hirsch Conjecture 4

So where are we? I guess we are trying all sorts of things, and perhaps we should try even more things. I find it very difficult to choose the more promising ideas, directions and comments as Tim Gowers and Terry Tao did so effectively in Polymath 1,4 and 5.  754 more words


Polymath 3: The Polynomial Hirsch Conjecture 2

Here we start the second research thread about the polynomial Hirsch conjecture.  I hope that people will feel as comfortable as possible to offer ideas about the problem. 207 more words

Open Problems

Polymath3 now active

Gil Kalai has officially started the Polymath3 project (Polynomial Hirsch conjecture) with a research thread at his blog.

The original aim of this project is to prove the polynomial Hirsch conjecture, which is a conjecture in the combinatorial geometry of polytopes.   180 more words