Tag Archives: Szemeredi’s theorem

An Open Discussion and Polls: Around Roth’s Theorem

Suppose that  is a subset of of maximum cardinality not containing an arithmetic progression of length 3. Let . How does behave? We do not really know. Will it help talking about it? Can we somehow look beyond the horizon and try to guess what … Continue reading

Posted in Combinatorics, Open discussion, Open problems | Tagged , , , | 29 Comments

Pushing Behrend Around

Erdos and Turan asked in 1936: What is the largest subset of {1,2,…,n} without a 3-term arithmetic progression? In 1946 Behrend found an example with  Now, sixty years later, Michael Elkin pushed the the factor from the denominator to the enumerator, … Continue reading

Posted in Combinatorics, Updates | Tagged , , | 14 Comments