Lecture: The Shifting Method

Endre Szemerédi

Abstract:

The shifting method is a counting technique. To understand it we are going to illustrate the method with three examples.

1) Arithmetic progressions of length 3.
2) Ramsey-‐type problem in additive combinatorics.
3) Giving a tight bound for the size of a set S ⊂ [1, N] having the property that for every x, y ∈ S, x +y ≠ Z².

Part of the work is a joint work with S. Herdade and A. Khalfalah.
No prior knowledge is assumed.

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