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 Friendship and Sesame, Maryam and Marina, Israel and Iran
 Elchanan Mossel’s Amazing Dice Paradox (your answers to TYI 30)
 TYI 30: Expected number of Dice throws
 Test your intuition 29: Diameter of various random trees
 Micha Perles’ Geometric Proof of the ErdosSos Conjecture for Caterpillars
 Touching Simplices and Polytopes: Perles’ argument
 Where were we?
 Call for nominations for the Ostrowski Prize 2017
 Problems for Imre Bárány’s Birthday!
Top Posts & Pages
 Elchanan Mossel's Amazing Dice Paradox (your answers to TYI 30)
 Friendship and Sesame, Maryam and Marina, Israel and Iran
 TYI 30: Expected number of Dice throws
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24
 The Race to Quantum Technologies and Quantum Computers (Useful Links)
 Touching Simplices and Polytopes: Perles' argument
 Test your intuition 29: Diameter of various random trees
 R(5,5) ≤ 48
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Category Archives: Combinatorics
Around the GarsiaStanley’s Partitioning Conjecture
Art Duval, Bennet Goeckner, Carly Klivans, and Jeremy Martin found a counter example to the GarsiaStanley partitioning conjecture for CohenMacaulay complexes. (We mentioned the conjecture here.) Congratulations Art, Bennet, Carly and Jeremy! Art, Carly, and Jeremy also wrote an article on the … Continue reading
Posted in Combinatorics, Geometry
Tagged Art Duval, Bennet Goeckner, Carly Klivans, GarsiaStanley conjecture, Jeremy Martin, Ping Zhang
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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
Posted in Combinatorics, Open problems, Updates
Tagged Brendan D. McKay, Vigleik Angeltveit
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Test Your Intuition (27) about the AlonTarsi Conjecture
On the occasion of Polymath 12 devoted to the Rota basis conjecture let me remind you about the AlonTarsi conjecture and test your intuition concerning a strong form of the conjecture. The sign of a Latin square is the product … Continue reading
Posted in Combinatorics, Open problems, Test your intuition
Tagged AlonTarsi conjecture, Polymath12
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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
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 CarloRota. Let me mention a strong version of Rota’s conjecture (Conjecture … Continue reading
Posted in Combinatorics, Mathematics over the Internet, Movies, Music, Sport, Updates
Tagged Polymath12
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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
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
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… GermanJewish 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
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 Boolean functions
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Laci Babai Visits Israel!
I am sure that every one of the readers of this blog heard about Laci Babai’s quasipolynomial algorithm for graph isomorphism and also the recent drama about it: A mistake pointed out by Harald Helfgott, a new subexponential but … Continue reading
Posted in Combinatorics, Computer Science and Optimization, Updates
Tagged graph isomorphism, Laszlo Babai
2 Comments