Jozsef at 01:17, 9 March 2009

2009-03-09T01:17:29Z

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	The [[corners theorem]] asserts that for every <math>\delta>0</math> there exists n such that every subset A of <math>[n]^2</math> of density at least <math>\delta</math> contains a corner.		The [[corners theorem]] asserts that for every <math>\delta>0</math> there exists n such that every subset A of <math>[n]^2</math> of density at least <math>\delta</math> contains a corner.

			In general, a corner is a subset of <math>[n]^m</math> of the form <math>\{(x_1,x_2,\ldots , x_m),(x_1+d,x_2,\ldots , x_m),(x_1,x_2+d,\ldots , x_m),\ldots ,(x_1,x_2,\ldots , x_m+d)\}</math> with <math>d\ne 0.</math>

			The Multidimensional Szemeredi's theorem (proved by Furstenberg and Katznelson) asserts that for every real <math>\delta>0</math> and integer <math>m>1</math> there exists n such that every subset A of <math>[n]^m</math> of density at least <math>\delta</math> contains a corner.

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2009-02-16T18:55:29Z

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A ''corner'' is a subset of <math>[n]^2</math> of the form <math>\{(x,y),(x+d,y),(x,y+d)\}</math> with <math>d\ne 0.</math> One often insists also that d should be positive.

The [[corners theorem]] asserts that for every <math>\delta>0</math> there exists n such that every subset A of <math>[n]^2</math> of density at least <math>\delta</math> contains a corner.

Corners - Revision history

Jozsef at 01:17, 9 March 2009

Gowers: Created article