Dyson’s transform in number theory
E17018
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Dyson’s transform in number theory canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T145464 — 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: Dyson’s transform in number theory Context triple: [Freeman Dyson, notableWork, Dyson’s transform in number theory]
-
A.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
B.
Dyson series
The Dyson series is a perturbative expansion in quantum field theory that expresses time-ordered exponentials and scattering amplitudes as an infinite series of integrals, each term corresponding to a Feynman diagram.
-
C.
Levine-Fricke Field
Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
-
D.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
-
E.
The Mathematical Theory of Black Holes
The Mathematical Theory of Black Holes is a landmark monograph that presents a rigorous, comprehensive treatment of the physics and mathematics underlying black hole solutions in general relativity.
- 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: Dyson’s transform in number theory Target entity description: Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
A.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
B.
Dyson series
The Dyson series is a perturbative expansion in quantum field theory that expresses time-ordered exponentials and scattering amplitudes as an infinite series of integrals, each term corresponding to a Feynman diagram.
-
C.
Levine-Fricke Field
Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
-
D.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
-
E.
The Mathematical Theory of Black Holes
The Mathematical Theory of Black Holes is a landmark monograph that presents a rigorous, comprehensive treatment of the physics and mathematics underlying black hole solutions in general relativity.
- F. None of above. chosen
Statements (28)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorial technique
ⓘ
construction in partition theory ⓘ tool in additive number theory ⓘ |
| appliesTo | integer partitions ⓘ |
| context | theory of integer partitions ⓘ |
| field |
combinatorics
ⓘ
mathematical physics ⓘ number theory ⓘ number theory ⓘ |
| goal |
to construct explicit correspondences between partition sets
ⓘ
to obtain combinatorial interpretations of analytic identities ⓘ |
| introducedBy | Freeman Dyson ⓘ |
| involves |
mapping partitions to other partitions
ⓘ
preserving combinatorial statistics under transformation ⓘ |
| knownFor | introducing Dyson’s transform in partition theory ⓘ |
| methodType |
bijective technique
ⓘ
combinatorial transformation ⓘ |
| namedAfter | Freeman Dyson ⓘ |
| notableFor | use in proofs of partition congruences ⓘ |
| purpose |
to manipulate integer partitions
ⓘ
to relate different families of partitions ⓘ to study partition congruences ⓘ to study partition identities ⓘ |
| relatedTo |
Dyson’s rank of a partition
ⓘ
Ramanujan partition congruences ⓘ Rogers–Ramanujan-type identities ⓘ |
| usedIn |
analysis of partition generating functions
ⓘ
combinatorial proofs of partition theorems ⓘ |
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: Dyson’s transform in number theory Description of subject: Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.