Szekeres configuration
E386033
The Szekeres configuration is a notable geometric arrangement in projective geometry consisting of points and lines with specific incidence properties, studied for its combinatorial and symmetry characteristics.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Szekeres configuration canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3757270 — 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: Szekeres configuration Context triple: [George Szekeres, notableWork, Szekeres configuration]
-
A.
Fano plane
The Fano plane is the smallest finite projective plane, consisting of seven points and seven lines with rich symmetrical and combinatorial properties.
-
B.
Conway circle theorem
The Conway circle theorem is a geometric result in triangle geometry that identifies a special circle associated with a triangle and certain constructed points, revealing notable collinearities and concyclicity relationships.
-
C.
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.
-
D.
Clebsch
Clebsch is a German surname most notably associated with mathematician Alfred Clebsch, known for his contributions to algebraic geometry and invariant theory.
-
E.
Plücker
Plücker is a German surname most notably associated with Julius Plücker, a 19th-century mathematician and physicist known for his contributions to analytic and projective geometry.
- 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: Szekeres configuration Target entity description: The Szekeres configuration is a notable geometric arrangement in projective geometry consisting of points and lines with specific incidence properties, studied for its combinatorial and symmetry characteristics.
-
A.
Fano plane
The Fano plane is the smallest finite projective plane, consisting of seven points and seven lines with rich symmetrical and combinatorial properties.
-
B.
Conway circle theorem
The Conway circle theorem is a geometric result in triangle geometry that identifies a special circle associated with a triangle and certain constructed points, revealing notable collinearities and concyclicity relationships.
-
C.
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.
-
D.
Clebsch
Clebsch is a German surname most notably associated with mathematician Alfred Clebsch, known for his contributions to algebraic geometry and invariant theory.
-
E.
Plücker
Plücker is a German surname most notably associated with Julius Plücker, a 19th-century mathematician and physicist known for his contributions to analytic and projective geometry.
- F. None of above. chosen
Statements (26)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorial configuration
ⓘ
configuration in projective geometry ⓘ finite incidence structure ⓘ |
| appearsIn |
literature on combinatorial configurations
ⓘ
research on symmetric incidence structures ⓘ |
| field |
combinatorial geometry
ⓘ
projective geometry ⓘ |
| hasAspect |
combinatorial properties
ⓘ
symmetry properties ⓘ |
| hasIncidenceStructure |
lines
ⓘ
points ⓘ specified point–line incidences ⓘ |
| hasMotivation | understanding constraints on point–line incidences in projective spaces ⓘ |
| hasProperty |
finite
ⓘ
highly symmetric ⓘ rigid incidence structure ⓘ |
| namedAfter | George Szekeres ⓘ |
| relatedTo |
block designs
ⓘ
finite projective planes ⓘ incidence graphs ⓘ |
| studiedFor |
automorphism group structure
ⓘ
extremal combinatorial behavior ⓘ |
| studiedIn | incidence geometry ⓘ |
| usedIn |
classification of small configurations
ⓘ
study of extremal configurations in projective geometry ⓘ study of point–line incidence structures ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Szekeres configuration Description of subject: The Szekeres configuration is a notable geometric arrangement in projective geometry consisting of points and lines with specific incidence properties, studied for its combinatorial and symmetry characteristics.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.