Carlson-Simpson theorem - Revision history

Teorth at 07:52, 16 February 2009

2009-02-16T07:52:14Z

← Older revision		Revision as of 00:52, 16 February 2009
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	'''Carlson-Simpson theorem''' (k=3): If <math>[3]^\omega := \bigcup_{n=0}^\infty [3]^n</math> is partitioned into finitely many color classes, then one of the color classes contains an infinite-dimensional [[combinatorial subspace]], i.e. another copy of <math>[3]^\omega</math>.		'''Carlson-Simpson theorem''' (k=3): If <math>[3]^\omega := \bigcup_{n=0}^\infty [3]^n</math> is partitioned into finitely many color classes, then one of the color classes contains an infinite-dimensional [[combinatorial subspace]], i.e. another copy of <math>[3]^\omega</math>.

	Implies the [[coloring Hales-Jewett theorem]]. ~~The k=2 version already implies [[Hindman's theorem]].~~		Implies the [[coloring Hales-Jewett theorem]].

	The Carlson-Simpson theorem and the [[Graham-Rothschild theorem]] have a common generalisation, [[Carlson's theorem]].		The Carlson-Simpson theorem and the [[Graham-Rothschild theorem]] have a common generalisation, [[Carlson's theorem]].

	Both the Carlson-Simpson theorem and Carlson's theorem are is used in the [[Furstenberg-Katznelson argument]].		Both the Carlson-Simpson theorem and Carlson's theorem are is used in the [[Furstenberg-Katznelson argument]].

Teorth at 02:14, 16 February 2009

2009-02-16T02:14:47Z

← Older revision		Revision as of 19:14, 15 February 2009
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	Implies the [[coloring Hales-Jewett theorem]]. The k=2 version already implies [[Hindman's theorem]].		Implies the [[coloring Hales-Jewett theorem]]. The k=2 version already implies [[Hindman's theorem]].

	The Carlson-Simpson theorem and the [[Graham-Rothschild theorem]] have a common generalisation, ~~the~~ [[Carlson~~-Simpson Graham-Rothschild~~ theorem]].		The Carlson-Simpson theorem and the [[Graham-Rothschild theorem]] have a common generalisation, [[Carlson's theorem]].

	Both the Carlson-Simpson theorem and ~~the~~ Carlson~~-Simpson Graham-Rothschild~~ theorem are is used in the [[Furstenberg-Katznelson argument]].		Both the Carlson-Simpson theorem and Carlson's theorem are is used in the [[Furstenberg-Katznelson argument]].

Teorth at 01:32, 16 February 2009

2009-02-16T01:32:51Z

← Older revision		Revision as of 18:32, 15 February 2009
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	Implies the [[coloring Hales-Jewett theorem]]. The k=2 version already implies [[Hindman's theorem]].		Implies the [[coloring Hales-Jewett theorem]]. The k=2 version already implies [[Hindman's theorem]].

	It is used in the [[Furstenberg-Katznelson argument]].		The Carlson-Simpson theorem and the [[Graham-Rothschild theorem]] have a common generalisation, the [[Carlson-Simpson Graham-Rothschild theorem]].

			Both the Carlson-Simpson theorem and the Carlson-Simpson Graham-Rothschild theorem are is used in the [[Furstenberg-Katznelson argument]].

Teorth at 22:23, 15 February 2009

2009-02-15T22:23:12Z

← Older revision		Revision as of 15:23, 15 February 2009
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	'''Carlson-Simpson theorem''' (k=3): If <math>[3]^\omega := \bigcup_{n=0}^\infty [3]^n</math> is partitioned into finitely many color classes, then one of the color classes contains an infinite-dimensional combinatorial subspace, i.e. another copy of <math>[3]^\omega</math>.		'''Carlson-Simpson theorem''' (k=3): If <math>[3]^\omega := \bigcup_{n=0}^\infty [3]^n</math> is partitioned into finitely many color classes, then one of the color classes contains an infinite-dimensional [[combinatorial subspace]], i.e. another copy of <math>[3]^\omega</math>.

	Implies the [[coloring Hales-Jewett theorem]]. The k=2 version already implies Hindman's theorem.		Implies the [[coloring Hales-Jewett theorem]]. The k=2 version already implies [[Hindman's theorem]].

	It is used in the [[Furstenberg-Katznelson argument]].		It is used in the [[Furstenberg-Katznelson argument]].

Teorth at 17:23, 14 February 2009

2009-02-14T17:23:23Z

← Older revision		Revision as of 10:23, 14 February 2009
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	'''Carlson-Simpson theorem''' (k=3): If <math>[3]^\omega := \bigcup_{n=0}^\infty [3]^n</math> is partitioned into finitely many color classes, then one of the color classes contains an infinite-dimensional combinatorial subspace, i.e. another copy of <math>[3]^\omega</math>.		'''Carlson-Simpson theorem''' (k=3): If <math>[3]^\omega := \bigcup_{n=0}^\infty [3]^n</math> is partitioned into finitely many color classes, then one of the color classes contains an infinite-dimensional combinatorial subspace, i.e. another copy of <math>[3]^\omega</math>.

	Implies the [[coloring Hales-Jewett theorem]] ~~and~~ Hindman's theorem.		Implies the [[coloring Hales-Jewett theorem]]. The k=2 version already implies Hindman's theorem.

	It is used in the [[Furstenberg-Katznelson argument]].		It is used in the [[Furstenberg-Katznelson argument]].

Teorth: New page: '''Carlson-Simpson theorem''' (k=3): If $[3]^\omega := \bigcup_{n=0}^\infty [3]^n$ is partitioned into finitely many color classes, then one of the color classes contains an inf...

2009-02-14T17:22:45Z

New page: '''Carlson-Simpson theorem''' (k=3): If <math>[3]^\omega := \bigcup_{n=0}^\infty [3]^n</math> is partitioned into finitely many color classes, then one of the color classes contains an inf...

New page

'''Carlson-Simpson theorem''' (k=3): If <math>[3]^\omega := \bigcup_{n=0}^\infty [3]^n</math> is partitioned into finitely many color classes, then one of the color classes contains an infinite-dimensional combinatorial subspace, i.e. another copy of <math>[3]^\omega</math>.

Implies the [[coloring Hales-Jewett theorem]] and Hindman's theorem.

It is used in the [[Furstenberg-Katznelson argument]].