Hirsch (izquierda), autor de la conjetura que lleva su nombre; Klee (derecha) demostró, junto con Walkup, su equivalencia con la Conjetura de los d pasos. Hace unos días en el blog de Gil Kalai se hacían eco de la refutación de la conjetura de Hirsch por parte del matemático español Francisco. Sitio web institucional de la Universidad de Oviedo. Un catedrático asegura haber refutado la conjetura de Hirsch. 27/05/ – La Nueva España. Descargar.

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Francisco Santos encuentra un contraejemplo que refuta la conjetura de Hirsch | Gaussianos

Although Victor Klee was already retired—he was 76 years old—he came to the Department of Mathematics to talk to me. I have later found out that he asked the same question to many people, including all his students, but the question and the way it was posed made me feel special at that time. This talk is the answer to that question. ed

I will describe the construction of a dimensional polytope with 86 facets and diameter bigger than We had quite a few posts regarding the Hirsch conjecture and related problems.

Congrats to Paco; I look forward to seeing the talk in Seattle! This still leaves open the original Polymath3 question of whether the polynomial Hirsch conjecture is true and all that implies.

I was on sabbatical in the west coast in the fall of Davis and then in the fall of Berkeleyand I have mixed the two! OMG, I need to resubmit my abstract. I am afraid my construction conietura nothing about the polynomiality. I hope that is not true.

We chatted briefly in Seattle. This is a wonderful achievement. I hope I can make it to your talk. Seattle in July is absolutely delightful in stark contrast to November. I have checked old emails and Hrsch can now confirm that my talk at UW was in Janyary 22, Is this an explicit construction? Can you just list the coordinates of the vertices and identify the two that violate the conjecture?

Francisco Santos Leal

Out of curiosity, do you have any guesses on what the minimum dimension of a counterexample will turn out to be? I will risk some numbers: Part 1 is totally explicit conjethra has been verified with computer software polymake.

Part 2 is not explicit. On the other hand there is the problem that this polytope will be huge.


[] Sobre un contraejemplo a la conjetura de Hirsch

My estimate is it may have a billion vertices. I am not sure whether it is within our current computational capabilities to compute its diameter. As a final remark, may I recommend those wanting to know more about the state-of-the-art prior conjetyra this week to look at my recent survey http: How small ve the perturbations?

We know that the Hirsch conjecture could be reduced to simple polytopes, and the abstract versions usually conjetyra the dual formulation in terms of simplicial polytopes. In addition to the survey that Paco mentioned on his posting, you may be interested to know that there will be a workshop on the topic, to take place at IPAM UCLA, on January 18 — 21, I agree with Gil that there are plenty of interesting questions left and Paco just put more wood in the fire!!

As Jesus and others have said or implied, if anything, this very nice result will spur interest in discovering stronger worse examples and maybe even improved upper bounds ve the diameter. Several days have passed since my last post and I know some of you may be impatient to see the counter-example.

I am sorry to say that last and this week are being extremely busy for me, not only because of Hirsch; I am right now at a conference in which I am one of the main organizers http: A draft of my paper already exists and has been circulated among some ten people, including Gil Kalai.

I have put myself a hard deadline of May 24 for the release of the first public version. For the first iterations I can or could, I have not done it control the size of them, but the perturbations will need to be smaller and smaller, probably exponentially so, as we go along the 38 steps that are needed to go from dim 5 to dim There is actually a group of young enthusiasts among my beta-readers who are trying to find coordinates for the dim gadget, but the results they have so far are not very encouraging.

Experimentally we observe that:. Many thanks for this update. There is no reason for impatience, after all we waited 53 years, so we can wait a few more weeks. The beta-version of the paper looks very good.

Having constructions which depend on smaller and smaller perturbations may very well be necessary. Commenting on joint research with J. Prabhu said something like: Are we now getting some new insight regarding the abundance of counterexamples? Francisco Santos encuentra un contraejemplo que refuta la conjetura de Hirsch Gaussianos. The preprint is finally out. I am sorry about the delay, but several things happened to me while I was busy making other plans….


I want to have a contact to you by phone or email. Your pentaspacial model, as I red in magazine Tiempo, Madrid were I used to write for is more important than you believe.

I tell you when talk each other. Efficiency of the Simplex Method: Quo vadis Hirsch conjecture? Hirsch Conjecture 3 Euclidean Ramsey Theory. Hirsch Conjecture 2 Euclidean Ramsey Theory. You are commenting using your WordPress. You are commenting using your Twitter account. You are commenting using your Facebook account. Notify me of new comments via email. Notify me of new posts via email. Test Your Intuition Francisco Santos, Universidad de Cantabria Abstract: Facebook Reddit Twitter Google.

This entry was posted in Convex polytopesOpen problemsPolymath3.

May 10, at 9: May 10, at Tarantino from Stanford says: May 11, at 3: May 11, at 4: May 11, at 8: May 11, at May 11, at 5: May 11, at 9: May 12, at 2: May 12, at 5: May 12, at 8: I was working on the same problem.

I guess I need to find a new research topic. May 12, at May 12, at 3: May 13, at Jesus De Loera says: May 14, at May 14, hirdch 5: May 17, at 6: Hello everyone, Several days have passed since my last post and I know some of you may be impatient to see the counter-example.

Experimentally we observe that: May 17, at 9: Dear Paco, Many thanks for this update. May 19, at June 15, at I am sorry about the delay, but several things happened to me while I was busy making other plans… See http: September 29, at 5: Mi email address cmedinarebolledo yahoo. November 15, at 3: Leave a Reply Cancel reply Enter your comment here Fill in uirsch details below or click an icon to log in: Email required Address never made public.

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