Monthly Archives: September 2008

Extremal Combinatorics III: Some Basic Theorems

. Shattering Let us return to extremal problems for families of sets and describe several basic theorems and basic open problems. In the next part we will discuss a nice proof technique called “shifting” or “compression.” The Sauer-Shelah (-Perles -Vapnik-Chervonenkis) Lemma: (Here we write .) … Continue reading

Posted in Combinatorics, Open problems | Tagged , | 8 Comments

New Haven (mainly pictures)

]  Yale, New Haven   I am back in New Haven which have become my home away from home in the last five years.      Cappuccino’S and more – Cedar cross Congress, New Haven. Not only that this name is similar … Continue reading

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Annotating Kimmo Eriksson’s Poem

“Start counting her NUMBER OF FACES,” Kimmo Eriksson, Brush up your Björner (2008). The time is right to annotate Kimmo Eriksson’s memorable poem: 1. What are Chip firing games? Many women will find it admirable if you tell her she … Continue reading

Posted in Combinatorics, Poetry | Tagged , , , , , , , , , , | 7 Comments

A Diameter Problem (5)

6. First subexponential bounds.  Proposition 1: How to prove it: This is easy to prove: Given two sets and in our family , we first find a path of the form where, and . We let with and consider the family … Continue reading

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Diameter Problem (4)

Let us consider another strategy to deal with our diameter problem. Let us try to associate other graphs to our family of sets. Recall that we consider a family of subsets of size  of the set . Let us now associate  … Continue reading

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Diameter Problem (3)

3. What we will do in this post and and in future posts We will now try all sorts of ideas to give good upper bounds for the abstract diameter problem that we described. As we explained, such bounds apply … Continue reading

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Oded

  I just heard the terrible news that Oded Schramm was killed in a hiking accident. Oded was hiking on Guye Peak near Snoqualmie Pass near Seattle. This is a terrible loss to Oded’s family, and our hearts and thoughts are … Continue reading

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The Prisoner’s Dilemma, Sympathy, and Yaari’s Challenge

Correlation and Cooperation In our spring school devoted to Arrow’s economics, Menahem Yaari gave a talk  entitled “correlation and cooperation.” It was about games as a model of people’s behavior, and Yaari made the following points: It is an empirical fact … Continue reading

Posted in Economics, Games, Philosophy, Rationality | Tagged , , | 2 Comments