Author Archives: Gil Kalai

R(5,5) ≤ 48

The Ramsey numbers R(s,t) The Ramsey number R(s, t) is defined to be the smallest n such that every graph of order n contains either a clique of s vertices or an independent set of t vertices. Understanding the values … Continue reading

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Test Your Intuition (27) about the Alon-Tarsi Conjecture

On the occasion of Polymath 12 devoted to the Rota basis conjecture let me remind you about the Alon-Tarsi conjecture and test your intuition concerning a strong form of the conjecture. The sign of a Latin square is the product … Continue reading

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Thilo Weinert: Transfinite Ramsey Numbers

This is first of three posts kindly written by Thilo Weinert Recently Gil asked me whether I would like to contribute to his blog and I am happy to do so. I enjoy both finite and infinite combinatorics and it … Continue reading

Posted in Combinatorics, Guest post, Logic and set theory | Tagged | 3 Comments

Timothy Chow Launched Polymath12 on Rota Basis Conjecture and Other News

Polymath12 Timothy Chow launched polymath12 devoted to the Rota Basis conjecture on the polymathblog. A classic paper on the subject is the 1989 paper by Rosa Huang and Gian Carlo-Rota. Let me mention a strong version of Rota’s conjecture (Conjecture … Continue reading

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Proof By Lice!

From camels to lice. (A proof promised here.) Theorem (Hopf and Pannwitz, 1934): Let be a set of points in the plane  in general position (no three points on a line) and consider line segments whose endpoints are in .  Then … Continue reading

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The seventeen camels riddle, and Noga Alon’s camel proof and algorithms

Three children inherited 17 camels. The will gave one half to one child, one third to a second child and one ninth to the third. The children did not know what to do and  a neighbor offered to lend them … Continue reading

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Edmund Landau and the Early Days of the Hebrew University of Jerusalem

Some personal/historical remarks in  first minutes of my lecture at 7ECM on July 2016… German-Jewish mathematicians in the early days of the Hebrew University of Jerusalem Being invited to give a plenary lecture at the 7ECM was a great honor … Continue reading

Posted in Academics, Combinatorics, personal | Tagged | 4 Comments

Boolean Functions: Influence, Threshold, and Noise

Here is the written version of my address at the 7ECM last July in Berlin. Boolean functions, Influence, threshold, and Noise Trying to follow an example of a 1925 lecture by Landau (mentioned in the lecture), the writing style is very … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Probability | Tagged | 7 Comments

Laci Babai Visits Israel!

  I am sure that every one of the readers of this blog heard about Laci Babai’s quasi-polynomial algorithm for graph isomorphism and also the recent drama about it: A mistake pointed out by Harald Helfgott,  a new sub-exponential but … Continue reading

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Polymath10 conclusion

The Polymath10 project on the Erdos-Rado Delta-System conjecture took place over this blog from November 2015 to May 2016. I aimed for an easy-going project that people could participate calmly aside from their main research efforts and  the duration of … Continue reading

Posted in Combinatorics, Open problems, Polymath10 | Tagged , | 4 Comments