Bose–Nair theorem
E886601
The Bose–Nair theorem is a result in combinatorial design theory that provides conditions for the existence and construction of certain balanced incomplete block designs, contributing to the foundations of modern combinatorics and coding theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Bose–Nair theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10803781 — 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: Bose–Nair theorem Context triple: [Raj Chandra Bose, notableWork, Bose–Nair theorem]
-
A.
Kesten’s theorem
Kesten’s theorem is a fundamental result in probability theory that characterizes when a random walk on a group is transient or recurrent, with deep implications for random walks on groups and percolation theory.
-
B.
Busemann–Feller theorem
The Busemann–Feller theorem is a result in geometric measure theory that characterizes when a metric space is geodesic by relating distance properties to the existence of shortest paths between points.
-
C.
Szekeres–Lindström theorem
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.
-
D.
Banach–Saks theorem
The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
-
E.
Birkhoff–von Neumann theorem
The Birkhoff–von Neumann theorem is a fundamental result in matrix theory and combinatorics stating that every doubly stochastic matrix can be expressed as a convex combination of permutation matrices.
- 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: Bose–Nair theorem Target entity description: The Bose–Nair theorem is a result in combinatorial design theory that provides conditions for the existence and construction of certain balanced incomplete block designs, contributing to the foundations of modern combinatorics and coding theory.
-
A.
Kesten’s theorem
Kesten’s theorem is a fundamental result in probability theory that characterizes when a random walk on a group is transient or recurrent, with deep implications for random walks on groups and percolation theory.
-
B.
Busemann–Feller theorem
The Busemann–Feller theorem is a result in geometric measure theory that characterizes when a metric space is geodesic by relating distance properties to the existence of shortest paths between points.
-
C.
Szekeres–Lindström theorem
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.
-
D.
Banach–Saks theorem
The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
-
E.
Birkhoff–von Neumann theorem
The Birkhoff–von Neumann theorem is a fundamental result in matrix theory and combinatorics stating that every doubly stochastic matrix can be expressed as a convex combination of permutation matrices.
- F. None of above. chosen
Statements (25)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
result in combinatorial design theory ⓘ |
| appliesTo |
block designs with specified balance properties
ⓘ
finite incidence structures ⓘ |
| area | discrete mathematics ⓘ |
| contributesTo |
foundations of coding theory
ⓘ
foundations of modern combinatorics ⓘ |
| field |
coding theory
ⓘ
combinatorial design theory ⓘ combinatorics ⓘ |
| namedAfter |
R. C. Bose
ⓘ
linked to:
Raj Chandra Bose
R. Nair ⓘ |
| provides |
conditions for construction of certain balanced incomplete block designs
ⓘ
conditions for existence of certain balanced incomplete block designs ⓘ |
| relatedTo |
balanced incomplete block design
ⓘ
finite geometry ⓘ t-design ⓘ |
| subject |
balanced incomplete block designs
ⓘ
block designs ⓘ construction of designs ⓘ existence of designs ⓘ |
| typeOfResult |
construction theorem
ⓘ
existence theorem ⓘ |
| usedIn |
construction of combinatorial designs with specified parameters
ⓘ
design of error-correcting codes ⓘ |
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: Bose–Nair theorem Description of subject: The Bose–Nair theorem is a result in combinatorial design theory that provides conditions for the existence and construction of certain balanced incomplete block designs, contributing to the foundations of modern combinatorics and coding theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.