Search Results for: Hirsch

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

Posted on April 13, 2011 by

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. Our research so far was … Continue reading →

Posted in Convex polytopes, Geometry, Polymath3 | Tagged , , | 37 Comments

Remote Blogging: Efficiency of the Simplex Method: Quo vadis Hirsch conjecture?

Posted on January 18, 2011 by

Here are some links and posts related to some of the talks in IPAM’s workshop “Efficiency of the Simplex Method: Quo vadis Hirsch conjecture?“ I will be happy to add links to pdf’s of the presentations and to relevant papers. Descriptions and … Continue reading →

Posted in Computer Science and Optimization, Conferences, Convex polytopes | 3 Comments

Polynomial Hirsch Conjecture 5: Abstractions and Counterexamples.

Posted on November 28, 2010 by

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. (And a related version about families of multisets.) The … Continue reading →

Posted in Open discussion, Open problems, Polymath3 | Tagged , | 59 Comments

Polymath3: Polynomial Hirsch Conjecture 4

Posted on October 21, 2010 by

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 … Continue reading →

Posted in Combinatorics, Convex polytopes, Open discussion, Open problems, Polymath3 | Tagged , | 73 Comments

Polymath3 : Polynomial Hirsch Conjecture 3

Posted on October 10, 2010 by

Here is the third research thread for the polynomial Hirsch conjecture.  I hope that people will feel as comfortable as possible to offer ideas about the problem we discuss. Even more important, to think about the problem either in the directions suggested by … Continue reading →

Posted in Combinatorics, Convex polytopes, Open discussion, Open problems, Polymath3 | Tagged | 102 Comments

Polymath 3: The Polynomial Hirsch Conjecture 2

Posted on October 3, 2010 by

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. The combinatorial problem looks simple and also everything that we know about it is rather simple: … Continue reading →

Posted in Convex polytopes, Open discussion, Open problems, Polymath3 | Tagged , | 104 Comments

Polymath 3: Polynomial Hirsch Conjecture

Posted on September 29, 2010 by

I would like to start here a research thread of the long-promised Polymath3 on the polynomial Hirsch conjecture. I propose to try to solve the following purely combinatorial problem. Consider t disjoint families of subsets of {1,2,…,n}, . Suppose that … Continue reading →

Posted in Convex polytopes, Open discussion, Open problems, Polymath3 | Tagged , | 117 Comments

IPAM Workshop – Efficiency of the Simplex Method: Quo vadis Hirsch conjecture?

Posted on July 8, 2010 by

  Workshop at IPAM: January 18 – 21, 2011 Here is the link to the IPAM conference. 

Posted in Combinatorics, Computer Science and Optimization, Conferences, Convex polytopes | Leave a comment

The Polynomial Hirsch Conjecture: The Crux of the Matter.

Posted on June 19, 2010 by

 Consider t disjoint families of subsets of {1,2,…,n}, .   Suppose that (*) For every , and every and , there is  which contains .  The basic question is: How large can t  be???   Let’s call the answer f(n).   … Continue reading →

Posted in Combinatorics, Convex polytopes, Open problems, Polymath3 | 5 Comments

“A Counterexample to the Hirsch Conjecture,” is Now Out

Posted on June 15, 2010 by

  Francisco (Paco) Santos’s paper “A Counterexample to the Hirsch Conjecture” is now out:  For some further information and links to the media see also this page. Here is a link to a TV interview. Abstract: The Hirsch Conjecture (1957) … Continue reading →

Posted in Convex polytopes | Tagged , | 2 Comments