Carlson-Simpson theorem: Difference between revisions
From Polymath Wiki
Jump to navigationJump to search
No edit summary |
No edit summary |
||
| Line 3: | Line 3: | ||
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]]. | |||
Both the Carlson-Simpson theorem and the Carlson-Simpson Graham-Rothschild theorem are is used in the [[Furstenberg-Katznelson argument]]. | |||
Revision as of 17:32, 15 February 2009
Carlson-Simpson theorem (k=3): If [math]\displaystyle{ [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]\displaystyle{ [3]^\omega }[/math].
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.
Both the Carlson-Simpson theorem and the Carlson-Simpson Graham-Rothschild theorem are is used in the Furstenberg-Katznelson argument.
