van der Waerden theorem
E1173842
UNEXPLORED
The van der Waerden theorem is a fundamental result in Ramsey theory stating that any finite coloring of the positive integers contains arbitrarily long monochromatic arithmetic progressions.
All labels observed (2)
| Label | Occurrences |
|---|---|
| van der Waerden’s theorem | 2 |
| van der Waerden theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T15741743 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: van der Waerden theorem Context triple: [Ramsey theory, hasCentralConcept, van der Waerden theorem]
-
A.
Szemerédi's theorem
Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
-
B.
Graham–Rothschild theorem
The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
-
C.
Steinhaus theorem
The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
-
D.
Roth theorem
Roth's theorem is a fundamental result in Diophantine approximation that gives an essentially optimal bound on how well algebraic irrational numbers can be approximated by rational numbers.
-
E.
Ramsey theory
Ramsey theory is a branch of combinatorics that studies the conditions under which order or structure must appear within sufficiently large or complex mathematical objects.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: van der Waerden theorem Target entity description: The van der Waerden theorem is a fundamental result in Ramsey theory stating that any finite coloring of the positive integers contains arbitrarily long monochromatic arithmetic progressions.
-
A.
Szemerédi's theorem
Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
-
B.
Graham–Rothschild theorem
The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
-
C.
Steinhaus theorem
The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
-
D.
Roth theorem
Roth's theorem is a fundamental result in Diophantine approximation that gives an essentially optimal bound on how well algebraic irrational numbers can be approximated by rational numbers.
-
E.
Ramsey theory
Ramsey theory is a branch of combinatorics that studies the conditions under which order or structure must appear within sufficiently large or complex mathematical objects.
- F. None of above. chosen
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: van der Waerden theorem
linked to: van der Waerden theorem