Graham–Rothschild theorem
E748751
The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
result in Ramsey theory ⓘ |
| appliesTo |
combinatorial cubes
ⓘ
finite colorings ⓘ parameter sets ⓘ |
| characterizes | existence of large monochromatic structured subsets ⓘ |
| concerns |
colorings of combinatorial configurations
ⓘ
colorings of parameter words over finite alphabets ⓘ higher-dimensional combinatorial structures ⓘ parameter words ⓘ |
| field |
Ramsey theory
NERFINISHED
ⓘ
combinatorics ⓘ |
| frameworkFor | unifying various partition theorems ⓘ |
| generalizes |
Hales–Jewett theorem
NERFINISHED
ⓘ
classical partition theorems ⓘ van der Waerden’s theorem NERFINISHED ⓘ |
| guarantees | existence of monochromatic combinatorial substructures ⓘ |
| hasConcept |
parameter sets in combinatorics
ⓘ
structured monochromatic sets ⓘ |
| hasProperty |
finite version of an infinitary Ramsey principle
ⓘ
highly general framework for partition theorems ⓘ |
| implies |
Hales–Jewett theorem
NERFINISHED
ⓘ
van der Waerden’s theorem NERFINISHED ⓘ |
| introducedBy |
Bruce Rothschild
NERFINISHED
ⓘ
Ronald Graham NERFINISHED ⓘ |
| isPartOf | structural Ramsey theory NERFINISHED ⓘ |
| levelOfGenerality | higher-dimensional ⓘ |
| mathematicalDiscipline | discrete mathematics ⓘ |
| namedAfter |
Bruce Rothschild
NERFINISHED
ⓘ
Ronald Graham NERFINISHED ⓘ |
| relatedTo |
Gallai–Witt theorem
NERFINISHED
ⓘ
Hindman’s theorem NERFINISHED ⓘ Ramsey’s theorem NERFINISHED ⓘ |
| studiedIn |
Ramsey theory monographs
ⓘ
advanced combinatorics literature ⓘ |
| topic |
Ramsey-type phenomena
ⓘ
colorings of finite structures ⓘ combinatorial partitions ⓘ |
| type | partition theorem ⓘ |
| usedIn |
combinatorial number theory
ⓘ
higher-dimensional Ramsey theory NERFINISHED ⓘ theory of partition regularity ⓘ |
Referenced by (1)
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