Van der Waerden's theorem (for 3-term progressions)
GPTKB entity
Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
finite colorings of integers
|
| gptkbp:field |
gptkb:Ramsey_theory
combinatorics |
| gptkbp:generalizes |
gptkb:Schur's_theorem
|
| gptkbp:hasSpecialCase |
Van der Waerden's theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Van der Waerden's theorem (for 3-term progressions)
|
| gptkbp:implies |
existence of monochromatic arithmetic progressions in colorings of integers
|
| gptkbp:minimumProgressionLength |
3
|
| gptkbp:namedAfter |
gptkb:Bartel_Leendert_van_der_Waerden
|
| gptkbp:publicationYear |
1927
|
| gptkbp:publishedIn |
gptkb:Mathematische_Annalen
|
| gptkbp:relatedTo |
gptkb:Szemerédi's_theorem
|
| gptkbp:sentence |
For any positive integer r, there exists a least positive integer N such that any r-coloring of the integers {1, 2, ..., N} contains a monochromatic 3-term arithmetic progression.
|
| gptkbp:type |
existence theorem
|
| gptkbp:bfsParent |
gptkb:Roth's_Theorem
|
| gptkbp:bfsLayer |
8
|