Category Archives: Combinatorics

Levon Khachatrian’s Memorial Conference in Yerevan

Workshop announcement The National Academy of Sciences of Armenia together American University of Armenia are organizing a memorial workshop on extremal combinatorics, cryptography and coding theory dedicated to the 60th anniversary of the mathematician Levon Khachatrian.  Professor Khachatrian started his … Continue reading

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Amazing: Peter Keevash Constructed General Steiner Systems and Designs

Here is one of the central and oldest problems in combinatorics: Problem: Can you find a collection S of q-subsets from an n-element set X set so that every r-subset of X is included in precisely λ sets in the collection? … Continue reading

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Many triangulated three-spheres!

The news Eran Nevo and Stedman Wilson have constructed triangulations with n vertices of the 3-dimensional sphere! This settled an old problem which stood open for several decades. Here is a link to their paper How many n-vertex triangulations does the 3 … Continue reading

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NatiFest is Coming

The conference Poster as designed by Rotem Linial A conference celebrating Nati Linial’s 60th birthday will take place in Jerusalem December 16-18. Here is the conference’s web-page. To celebrate the event, I will reblog my very early 2008 post “Nati’s … Continue reading

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Analysis of Boolean Functions – Week 7

Lecture 11 The Cap Set problem We presented Meshulam’s  bound for the maximum number of elements in a subset A of not containing a triple x,y,x of distinct elements whose sum is 0. The theorem is analogous to Roth’s theorem … Continue reading

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Analysis of Boolean Functions week 5 and 6

Lecture 7 First passage percolation 1)  Models of percolation. We talked about percolation introduced by Broadbent and Hammersley in 1957. The basic model is a model of random subgraphs of a grid in n-dimensional space. (Other graphs were considered later as … Continue reading

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Analysis of Boolean Functions – week 4

Lecture 6 Last week we discussed two applications of the Fourier-Walsh plus hypercontractivity method and in this lecture we will discuss one additional application: The lecture was based on a 5-pages paper by Ehud Friedgut and Jeff Kahn: On the number … Continue reading

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Analysis of Boolean Functions – Week 3

Lecture 4 In the third week we moved directly to the course’s “punchline” – the use of Fourier-Walsh expansion of Boolean functions and the use of Hypercontractivity. Before that we  started with  a very nice discrete isoperimetric question on a … Continue reading

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Richard Stanley: How the Proof of the Upper Bound Theorem (for spheres) was Found

The upper bound theorem asserts that among all d-dimensional polytopes with n vertices, the cyclic polytope maximizes the number of facets (and k-faces for every k). It was proved by McMullen for polytopes in 1970, and by Stanley for general triangulations … Continue reading

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Analysis of Boolean functions – week 2

Post on week 1; home page of the course analysis of Boolean functions Lecture II: We discussed two important examples that were introduced by Ben-Or and Linial: Recursive majority and  tribes. Recursive majority (RM): is a Boolean function with variables … Continue reading

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