Category Archives: Combinatorics

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

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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

Looking Again at Erdős’ Discrepancy Problem

Over Gowers’s blog Tim and I will make an attempt to revisit polymath5. Last Autumn I prepared three posts on the problems and we decided to launch them now. The first post is here. Here is a related MathOverflow question. … Continue reading

Posted in Combinatorics, Mathematics over the Internet, Open problems | 2 Comments

Tokyo, Kyoto, and Nagoya

Near Nagoya: Firework festival; Kyoto: with Gunter Ziegler; with Takayuki Hibi, Hibi, Marge Bayer, Curtis Green and Richard Stanly; Tokyo: Peter Frankl; crowded crossing I just returned from a trip to Japan to the FPSAC 2012 at Nagoya and a … Continue reading

Posted in Combinatorics, Conferences, Convex polytopes | Tagged , , , | 2 Comments

Celebrations in Sweden and Norway

Celebrations for Endre, Jean and Terry Anders Bjorner presents the 2012 Crafoord Prize in Mathematics  I am in Sweden for two weeks to work with colleagues and to take part in two celebrations. Jean Bourgain and Terence Tao are the 2012 laureates … Continue reading

Posted in Academics, Combinatorics, Conferences, Updates | Tagged , , | 2 Comments

Galvin’s Proof of Dinitz’s Conjecture

Dinitz’ conjecture The following theorem was conjectured by Jeff Dinitz in 1979 and proved by Fred Galvin in 1994: Theorem: Consider an n by n square table such that in each cell (i,j) you have a set with n or more elements. … Continue reading

Posted in Combinatorics, Games | 4 Comments

Fractional Sylvester-Gallai

Avi Wigderson was in town and gave a beautiful talk about an extension of Sylvester-Gallai theorem. Here is a link to the paper: Rank bounds for design matrices with applications to combinatorial geometry and locally correctable codes by Boaz Barak, Zeev … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Geometry | Tagged , , , | 3 Comments

Ryan O’Donnell: Analysis of Boolean Function

Ryan O’Donnell has begun writing a book about Fourier analysis of Boolean functions and  he serializes it on a blog entiled Analysis of Boolean Function.  New sections appear on Mondays, Wednesdays, and Fridays. Besides covering the basic theory, Ryan intends to describe applications … Continue reading

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