Bailey chains
E440252
Bailey chains are iterative constructions in the theory of basic hypergeometric series that generate infinite families of Rogers–Ramanujan-type identities from an initial Bailey pair.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Bailey chains canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4437400 — 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: Bailey chains Context triple: [Rogers–Ramanujan-type identities, relatedTo, Bailey chains]
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A.
Bealings
Bealings is a small rural village and civil parish located in the English county of Suffolk.
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B.
Banabans
Banabans are an indigenous Micronesian people originally from the island of Banaba in present-day Kiribati, known for their displacement due to extensive phosphate mining during the 20th century.
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C.
Crescent
Crescent is a long-distance Amtrak passenger train that runs between New York City and New Orleans, serving major cities along the U.S. East Coast and Deep South.
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D.
Copperline
"Copperline" is a reflective folk-rock song by American singer-songwriter James Taylor, known for its nostalgic lyrics about his North Carolina childhood.
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E.
Banes
Banes is a coastal municipality in eastern Cuba’s Holguín Province, historically known for its sugar industry and archaeological sites.
- 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: Bailey chains Target entity description: Bailey chains are iterative constructions in the theory of basic hypergeometric series that generate infinite families of Rogers–Ramanujan-type identities from an initial Bailey pair.
-
A.
Bealings
Bealings is a small rural village and civil parish located in the English county of Suffolk.
-
B.
Banabans
Banabans are an indigenous Micronesian people originally from the island of Banaba in present-day Kiribati, known for their displacement due to extensive phosphate mining during the 20th century.
-
C.
Crescent
Crescent is a long-distance Amtrak passenger train that runs between New York City and New Orleans, serving major cities along the U.S. East Coast and Deep South.
-
D.
Copperline
"Copperline" is a reflective folk-rock song by American singer-songwriter James Taylor, known for its nostalgic lyrics about his North Carolina childhood.
-
E.
Banes
Banes is a coastal municipality in eastern Cuba’s Holguín Province, historically known for its sugar industry and archaeological sites.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
concept in basic hypergeometric series
ⓘ
mathematical construction ⓘ |
| appearsIn | theory of Rogers–Ramanujan continued fraction NERFINISHED ⓘ |
| appliedIn |
combinatorial q-series identities
ⓘ
derivation of partition identities ⓘ proofs of Rogers–Ramanujan-type identities ⓘ |
| basedOn | Bailey pairs NERFINISHED ⓘ |
| constructionType | iterative construction ⓘ |
| context | theory of basic hypergeometric series ⓘ |
| developedBy | George E. Andrews NERFINISHED ⓘ |
| field |
analytic number theory
ⓘ
basic hypergeometric series ⓘ combinatorics ⓘ partition theory ⓘ q-series ⓘ |
| generalizes | Bailey lemma NERFINISHED ⓘ |
| hasKeyStep | choice of parameters in Bailey lemma ⓘ |
| historicalRoot | Bailey pairs of W. N. Bailey NERFINISHED ⓘ |
| input | initial Bailey pair ⓘ |
| inspiredBy | work of W. N. Bailey ⓘ |
| introducedBy | George E. Andrews NERFINISHED ⓘ |
| mathematicalArea |
q-hypergeometric series
ⓘ
special functions ⓘ |
| methodology | iterative application of Bailey lemma ⓘ |
| namedAfter | W. N. Bailey NERFINISHED ⓘ |
| output |
infinite family of q-series identities
ⓘ
sequence of Bailey pairs ⓘ |
| property |
can be iterated indefinitely
ⓘ
each step produces a new Bailey pair ⓘ systematic way to generate q-series identities ⓘ |
| purpose | to generate infinite families of Rogers–Ramanujan-type identities ⓘ |
| relatedTo |
Andrews–Gordon identities
NERFINISHED
ⓘ
Bailey lattice ⓘ Bailey lemma ⓘ Bailey transform ⓘ Göllnitz–Gordon identities NERFINISHED ⓘ Rogers–Ramanujan identities NERFINISHED ⓘ Rogers–Ramanujan-type identities NERFINISHED ⓘ |
| requires | initial Bailey pair relative to a parameter ⓘ |
| toolFor | systematic generation of Rogers–Ramanujan-type series-product identities ⓘ |
| usedFor |
discovering new partition theorems
ⓘ
unifying proofs of classical q-series identities ⓘ |
| usesConcept |
basic hypergeometric series summations
ⓘ
q-Pochhammer symbol NERFINISHED ⓘ q-difference equations ⓘ |
| yearIntroducedApprox | 1970s ⓘ |
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: Bailey chains Description of subject: Bailey chains are iterative constructions in the theory of basic hypergeometric series that generate infinite families of Rogers–Ramanujan-type identities from an initial Bailey pair.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.