Hindman's theorem - Revision history

75.82.57.223 at 11:06, 21 May 2009

2009-05-21T11:06:29Z

← Older revision		Revision as of 04:06, 21 May 2009
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	'''Hindman's theorem''': If <math>[2]^\omega := \bigcup_{n=0}^\infty [2]^n</math> is finitely colored, then one of the color classes contain all elements of an infinite-dimensional [[combinatorial subspace]] which contain the digit 1, and such that none of the fixed digits of this subspace are equal to 1.		'''Hindman's theorem''': If <math>[2]^\omega := \bigcup_{n=0}^\infty [2]^n</math> is finitely colored, then one of the color classes contain all elements of an infinite-dimensional [[combinatorial subspace]] which contain the digit 1, and such that none of the fixed digits of this subspace are equal to 1.

	The generalization of this theorem ~~to higher~~ k is [[Carlson's theorem]]. Hindman's theorem also implies [[Folkman's theorem]].		The generalization of this theorem which replaces 2 with larger k is [[Carlson's theorem]]. Hindman's theorem also implies [[Folkman's theorem]].

Teorth at 07:51, 16 February 2009

2009-02-16T07:51:18Z

← Older revision		Revision as of 00:51, 16 February 2009
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	'''Hindman's theorem''': If <math>[2]^\omega := \bigcup_{n=0}^\infty [2]^n</math> is finitely colored, then one of the color classes contain an infinite-dimensional [[combinatorial subspace]], ~~i.e. another copy~~ of ~~<math>[2]^\omega</math>~~.		'''Hindman's theorem''': If <math>[2]^\omega := \bigcup_{n=0}^\infty [2]^n</math> is finitely colored, then one of the color classes contain all elements of an infinite-dimensional [[combinatorial subspace]] which contain the digit 1, and such that none of the fixed digits of this subspace are equal to 1.

	The generalization of this theorem to higher k is ~~the~~ [[Carlson~~-Simpson~~ theorem]]. Hindman's theorem also implies [[Folkman's theorem]].		The generalization of this theorem to higher k is [[Carlson's theorem]]. Hindman's theorem also implies [[Folkman's theorem]].

Teorth at 07:45, 16 February 2009

2009-02-16T07:45:30Z

← Older revision		Revision as of 00:45, 16 February 2009
Line 1:		Line 1:
	'''Hindman's theorem''': If <math>[2]^\omega := \bigcup_{n=0}^\infty [2]^n</math> is finitely colored, then one of the color classes contain an infinite-dimensional [[combinatorial subspace]], i.e. another copy of <math>[2]^\omega</math>.		'''Hindman's theorem''': If <math>[2]^\omega := \bigcup_{n=0}^\infty [2]^n</math> is finitely colored, then one of the color classes contain an infinite-dimensional [[combinatorial subspace]], i.e. another copy of <math>[2]^\omega</math>.

	The generalization of this theorem to higher k is the [[Carlson-Simpson theorem]].		The generalization of this theorem to higher k is the [[Carlson-Simpson theorem]]. Hindman's theorem also implies [[Folkman's theorem]].

Teorth: New page: '''Hindman's theorem''': If $[2]^\omega := \bigcup_{n=0}^\infty [2]^n$ is finitely colored, then one of the color classes contain an infinite-dimensional [[combinatorial subspac...

2009-02-15T22:25:06Z

New page: '''Hindman's theorem''': If <math>[2]^\omega := \bigcup_{n=0}^\infty [2]^n</math> is finitely colored, then one of the color classes contain an infinite-dimensional [[combinatorial subspac...

New page

'''Hindman's theorem''': If <math>[2]^\omega := \bigcup_{n=0}^\infty [2]^n</math> is finitely colored, then one of the color classes contain an infinite-dimensional [[combinatorial subspace]], i.e. another copy of <math>[2]^\omega</math>.

The generalization of this theorem to higher k is the [[Carlson-Simpson theorem]].

Hindman's theorem - Revision history

75.82.57.223 at 11:06, 21 May 2009

Teorth at 07:51, 16 February 2009

Teorth at 07:45, 16 February 2009

Teorth: New page: '''Hindman's theorem''': If [2]^\omega := \bigcup_{n=0}^\infty [2]^n is finitely colored, then one of the color classes contain an infinite-dimensional [[combinatorial subspac...

Teorth: New page: '''Hindman's theorem''': If $[2]^\omega := \bigcup_{n=0}^\infty [2]^n$ is finitely colored, then one of the color classes contain an infinite-dimensional [[combinatorial subspac...