Szekeres–Lindström theorem
E386034
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Szekeres–Lindström theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3757272 — 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–Lindström theorem Context triple: [George Szekeres, notableWork, Szekeres–Lindström theorem]
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A.
de Bruijn–van Aardenne–Ehrenfest theorem
The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
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B.
Sperner's lemma
Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
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C.
Ky Fan’s lemma
Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
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D.
Hamilton’s compactness theorem
Hamilton’s compactness theorem is a fundamental result in geometric analysis that provides conditions under which a sequence of Riemannian manifolds with controlled curvature and injectivity radius admits a smoothly convergent subsequence.
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E.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
- 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–Lindström theorem Target entity description: The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
-
A.
de Bruijn–van Aardenne–Ehrenfest theorem
The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
-
B.
Sperner's lemma
Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
-
C.
Ky Fan’s lemma
Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
-
D.
Hamilton’s compactness theorem
Hamilton’s compactness theorem is a fundamental result in geometric analysis that provides conditions under which a sequence of Riemannian manifolds with controlled curvature and injectivity radius admits a smoothly convergent subsequence.
-
E.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
- F. None of above. chosen
Statements (31)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorics theorem
ⓘ
mathematical theorem ⓘ |
| appliesTo | finite sets ⓘ |
| area | discrete mathematics ⓘ |
| characterizes | maximum size of intersecting families of subsets ⓘ |
| concerns | families of subsets with pairwise nonempty intersection ⓘ |
| field |
combinatorics
ⓘ
extremal set theory ⓘ |
| gives | upper bounds on the size of intersecting families ⓘ |
| hasConcept |
intersecting family
ⓘ
maximum intersecting family ⓘ set system ⓘ uniform family of sets ⓘ |
| hasProofTechnique |
combinatorial arguments
ⓘ
extremal methods ⓘ |
| is |
precursor of the Erdős–Ko–Rado theorem
ⓘ
special case of the Erdős–Ko–Rado theorem ⓘ |
| language | mathematical notation ⓘ |
| namedAfter |
Bernt Lindström
ⓘ
George Szekeres ⓘ |
| relatedTo |
Erdős–Ko–Rado theorem
ⓘ
Hilton–Milner theorem ⓘ
linked to:
Erdős–Ko–Rado theorem
|
| relationTo | Erdős–Ko–Rado theorem ⓘ |
| subject |
families of subsets
ⓘ
intersecting families of sets ⓘ |
| topic | intersection properties of set families ⓘ |
| typeOfResult | extremal bound ⓘ |
| usedIn |
coding theory
ⓘ
design theory ⓘ extremal combinatorics ⓘ graph theory ⓘ |
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–Lindström theorem Description of subject: The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.