Graham-Rothschild theorem: Difference between revisions
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New page: '''Graham-Rothschild theorem''' (k=3): If all the combinatorial lines in <math>[3]^n</math> is partitioned into c color classes, and n is sufficiently large depending on c, m, then the... |
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'''Graham-Rothschild theorem''' (k=3): If all the [[combinatorial | '''Graham-Rothschild theorem''' (k=3): If all the [[combinatorial line]]s in <math>[3]^n</math> is partitioned into c color classes, and n is sufficiently large depending on c, m, then there is an m-dimensional [[combinatorial subspace]] of <math>[3]^n</math> such that all the combinatorial lines in this subspace have the same color. | ||
This theorem implies the [[Hales-Jewett theorem]]. | This theorem implies the [[Hales-Jewett theorem]]. | ||
Revision as of 14:13, 15 February 2009
Graham-Rothschild theorem (k=3): If all the combinatorial lines in [math]\displaystyle{ [3]^n }[/math] is partitioned into c color classes, and n is sufficiently large depending on c, m, then there is an m-dimensional combinatorial subspace of [math]\displaystyle{ [3]^n }[/math] such that all the combinatorial lines in this subspace have the same color.
This theorem implies the Hales-Jewett theorem.
