The corners theorem, in arithmetic combinatorics, states that for any threshold epsilon greater than zero, a sufficiently large N by N grid has the property that any subset containing at least epsilon times N squared points must contain a corner, meaning three points of the form (x,y), (x+h,y) and (x,y+h) for some nonzero h. Miklós Ajtai and Endre Szemerédi first proved the result in 1974 using Szemerédi's theorem, and Jozsef Solymosi gave a shorter proof in 2003 using the triangle removal lemma.
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Source Corners theorem (Wikipedia)
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1. Corners theorem (Wikipedia)
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It was first proved by Miklós Ajtai and Endre Szemerédi in 1974
In Group: Enumerative, Additive and Algebraic Combinatorics, Lead
In arithmetic combinatorics, the corners theorem states that
- In Branch: Combinatorics, Lead sentence
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