Search Results for: Hirsch

Francisco Santos Disproves the Hirsch Conjecture

A title and an abstract for the conference “100 Years in Seattle: the mathematics of Klee and Grünbaum” drew a special attention: Title: “A counter-example to the Hirsch conjecture” Author: Francisco Santos, Universidad de Cantabria Abstract:  I have been in … Continue reading

Posted in Convex polytopes, Open problems, Polymath3 | 34 Comments

The Polynomial Hirsch Conjecture: Discussion Thread, Continued

Here is a  link for the just-posted paper Diameter of Polyhedra: The Limits of Abstraction by Freidrich Eisenbrand, Nicolai Hahnle,  Sasha Razborov, and Thomas Rothvoss. And here is a link to the paper  by Sandeep Koranne and Anand Kulkarni “The d-step Conjecture is Almost true”  – … Continue reading

Posted in Convex polytopes, Open discussion, Open problems | Tagged , | 16 Comments

The Polynomial Hirsch Conjecture: Discussion Thread

This post is devoted to the polymath-proposal about the polynomial Hirsch conjecture. My intention is to start here a discussion thread on the problem and related problems. (Perhaps identifying further interesting related problems and research directions.) Earlier posts are: The polynomial Hirsch … Continue reading

Posted in Convex polytopes, Open discussion, Open problems | Tagged , | 115 Comments

The Polynomial Hirsch Conjecture – How to Improve the Upper Bounds.

I can see three main avenues toward making progress on the Polynomial Hirsch conjecture. One direction is trying to improve the upper bounds, for example,  by looking at the current proof and trying to see if it is wasteful and if so where … Continue reading

Posted in Convex polytopes, Open discussion, Open problems | Tagged , | 14 Comments

The Polynomial Hirsch Conjecture, a Proposal for Polymath3 (Cont.)

The Abstract Polynomial Hirsch Conjecture A convex polytope is the convex hull of a finite set of points in a real vector space. A polytope can be described as the intersection of a finite number of closed halfspaces. Polytopes have … Continue reading

Posted in Convex polytopes, Open discussion, Open problems | Tagged , | 5 Comments

The Polynomial Hirsch Conjecture: A proposal for Polymath3

This post is continued here.  Eddie Kim and Francisco Santos have just uploaded a survey article on the Hirsch Conjecture. The Hirsch conjecture: The graph of a d-polytope with n vertices  facets has diameter at most n-d. We devoted several … Continue reading

Posted in Convex polytopes, Open discussion, Open problems | Tagged , , , | 38 Comments

Some old and new problems in combinatorics and geometry

Paul Erdős in Jerusalem, 1933  1993 I just came back from a great Erdős Centennial conference in wonderful Budapest. I gave a lecture on old and new problems (mainly) in combinatorics and geometry (here are the slides), where I presented twenty … Continue reading

Posted in Combinatorics, Geometry, Open problems | Tagged | 4 Comments

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.  Jesus de Loera and Steve Klee described simplicial polytopes which are not  … Continue reading

Posted in Convex polytopes, Guest blogger | Tagged , , , | Leave a comment

Some Updates

Jeff Kahn was in town: so we worked together also with Ehud Friedgut and Roy Meshulam (and others) quite intensively. Very nice! Stay tuned for a report! Polynomial Hirsch conjecture (polymath3): While the conjecture remains wide open there are some … Continue reading

Posted in Updates | 3 Comments

Günter Ziegler: 1000$ from Beverly Hills for a Math Problem. (IPAM remote blogging.)

Scanned letter by Zadeh. (c) Günter M. Ziegler left-to-right: David Avis, Norman Zadeh,  Oliver Friedmann, and Russ Caflish (IPAM director). Photo courtesy Eddie Kim. Update: The slides for Friedmann’s talk are now available. The conference schedule page contains now the slides for … Continue reading

Posted in Computer Science and Optimization, Conferences, Guest blogger | Tagged | 4 Comments