Szemerédi–Trotter theorem
E1536082
UNEXPLORED
The Szemerédi–Trotter theorem is a fundamental result in combinatorial geometry that gives near-optimal upper bounds on the number of incidences between points and lines in the plane.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Szemerédi–Trotter theorem canonical | 3 |
How this entity was disambiguated
This entity first appeared as the object of triple T22423294 — 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: Szemerédi–Trotter theorem Context triple: [Erdős distinct distances problem, relatedTo, Szemerédi–Trotter theorem]
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A.
Sylvester–Gallai theorem
The Sylvester–Gallai theorem is a result in incidence geometry stating that for any finite set of points in the Euclidean plane not all on a single line, there exists a line that passes through exactly two of the points.
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B.
Erdős distinct distances problem
The Erdős distinct distances problem is a famous question in combinatorial geometry that asks for the minimum number of distinct distances determined by a given number of points in the plane.
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C.
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.
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D.
Erdős–Szekeres theorem
The Erdős–Szekeres theorem is a fundamental result in combinatorial geometry that guarantees the existence of large convex polygons within sufficiently large sets of points in the plane in general position.
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E.
de Bruijn–Erdős theorem
The de Bruijn–Erdős theorem is a fundamental result in combinatorics and graph theory that relates finite and infinite structures, notably asserting that certain properties of infinite graphs or set systems are determined by their finite substructures.
- 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: Szemerédi–Trotter theorem Target entity description: The Szemerédi–Trotter theorem is a fundamental result in combinatorial geometry that gives near-optimal upper bounds on the number of incidences between points and lines in the plane.
-
A.
Sylvester–Gallai theorem
The Sylvester–Gallai theorem is a result in incidence geometry stating that for any finite set of points in the Euclidean plane not all on a single line, there exists a line that passes through exactly two of the points.
-
B.
Erdős distinct distances problem
The Erdős distinct distances problem is a famous question in combinatorial geometry that asks for the minimum number of distinct distances determined by a given number of points in the plane.
-
C.
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.
-
D.
Erdős–Szekeres theorem
The Erdős–Szekeres theorem is a fundamental result in combinatorial geometry that guarantees the existence of large convex polygons within sufficiently large sets of points in the plane in general position.
-
E.
de Bruijn–Erdős theorem
The de Bruijn–Erdős theorem is a fundamental result in combinatorics and graph theory that relates finite and infinite structures, notably asserting that certain properties of infinite graphs or set systems are determined by their finite substructures.
- F. None of above. chosen
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.