Category Archives: Combinatorics

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

Andriy Bondarenko Showed that Borsuk’s Conjecture is False for Dimensions Greater Than 65!

The news in brief Andriy V. Bondarenko proved in his remarkable paper The Borsuk Conjecture for two-distance sets  that the Borsuk’s conjecture is false for all dimensions greater than 65. This is a substantial improvement of the earlier record (all dimensions … Continue reading

Posted in Combinatorics, Geometry, Open problems | Tagged , , , , | 2 Comments

New Ramanujan Graphs!

Margulis’ paper Ramanujan graphs were constructed independently by Margulis and by Lubotzky, Philips and Sarnak (who also coined the name). The picture above shows Margulis’ paper where the graphs are defined and their girth is studied. (I will come back to the question … Continue reading

Posted in Algebra and Number Theory, Combinatorics, Open problems | Tagged | 10 Comments

Andrei

Andrei Zelevinsky passed away a week ago on April 10, 2013, shortly after turning sixty. Andrei was a great mathematician and a great person. I first met him in a combinatorics conference in Stockholm 1989. This was the first major … Continue reading

Posted in Algebra and Number Theory, Combinatorics, Obituary | Tagged | 5 Comments

Test Your Intuition (19): The Advantage of the Proposers in the Stable Matching Algorithm

Stable mariage The Gale-Shapley stable matching theorem and the algorithm. GALE-SHAPLEY THEOREM Consider a society of n men and n women and suppose that every man [and every woman] have a preference (linear) relation on the women [men] he [she] knows. Then … Continue reading

Posted in Combinatorics, Games, Probability, Test your intuition | Tagged , , , , , , | 7 Comments

Erdős’ Birthday

Paul Erdős was born on March 26, 1913 2013 a hundred years ago. This picture (from Ehud Friedgut’s homepage) was taken in September ’96 in a Chinese restaurant in Warsaw, a few days before Paul Erdős passed away. The other diners are Svante Janson, Tomasz Łuczack and … Continue reading

Posted in Combinatorics | Tagged | 3 Comments

F ≤ 4E

1. E ≤ 3V Let G be a simple planar graph with V vertices and E edges. It follows from Euler’s theorem that E ≤ 3V In fact, we have (when V is at least 3,) that E ≤ 3V – 6. … Continue reading

Posted in Combinatorics, Convex polytopes, Geometry, Open problems | Tagged | 12 Comments

Lionel Pournin found a combinatorial proof for Sleator-Tarjan-Thurston diameter result

I just saw in Claire Mathieu’s blog  “A CS professor blog” that a simple proof of the Sleator-Tarjan-Thurston’s diameter result for the graph of the associahedron was found by Lionel Pournin! Here are slides of his lecture “The diameters of associahedra” … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Convex polytopes | Tagged , | 1 Comment

Happy Birthday Ron Aharoni!

Ron Aharoni, one of Israel’s and the world’s leading combinatorialists celebrated his birthday last month. This is a wonderful opportunity to tell you about a few of the things that Ron did mainly around matching theory. Menger’s theorem for infinite … Continue reading

Posted in Combinatorics, Happy birthday | Tagged , , , , | 1 Comment

The Quantum Debate is Over! (and other Updates)

Quid est noster computationis mundus? Nine months after is started, (much longer than expected,) and after eight posts on GLL, (much more than planned,)  and almost a thousand comments of overall good quality,   from quite a few participants, my … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Controversies and debates, Updates | Tagged , , | 3 Comments