Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:category |
arithmetic combinatorics
theorems in Ramsey theory |
| gptkbp:field |
gptkb:Ramsey_theory
combinatorics |
| https://www.w3.org/2000/01/rdf-schema#label |
van der Waerden's theorem
|
| gptkbp:namedAfter |
gptkb:Bartel_Leendert_van_der_Waerden
|
| gptkbp:publishedIn |
gptkb:Mathematische_Annalen
|
| gptkbp:relatedTo |
gptkb:Ramsey's_theorem
gptkb:Szemerédi's_theorem |
| gptkbp:sentence |
For any given positive integers k and r, there exists a minimum number N such that any r-coloring of the integers {1, 2, ..., N} contains a monochromatic arithmetic progression of length k.
|
| gptkbp:yearProved |
1927
|
| gptkbp:bfsParent |
gptkb:B.L._van_der_Waerden
gptkb:Bartel_Leendert_van_der_Waerden gptkb:Ramsey's_theorem gptkb:Ramsey_theory gptkb:Szemerédi's_theorem |
| gptkbp:bfsLayer |
5
|