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
ⓘ
linked to:
Rogers–Ramanujan-type identities
|
| appliedIn |
combinatorial q-series identities
ⓘ
derivation of partition identities ⓘ proofs of Rogers–Ramanujan-type identities ⓘ |
| basedOn | Bailey pairs ⓘ |
| constructionType | iterative construction ⓘ |
| context | theory of basic hypergeometric series ⓘ |
| developedBy | George E. Andrews ⓘ |
| field |
analytic number theory
ⓘ
basic hypergeometric series ⓘ combinatorics ⓘ partition theory ⓘ q-series ⓘ |
| generalizes | Bailey lemma ⓘ |
| hasKeyStep | choice of parameters in Bailey lemma ⓘ |
| historicalRoot | Bailey pairs of W. N. Bailey ⓘ |
| input | initial Bailey pair ⓘ |
| inspiredBy | work of W. N. Bailey ⓘ |
| introducedBy | George E. Andrews ⓘ |
| mathematicalArea |
q-hypergeometric series
ⓘ
special functions ⓘ |
| methodology | iterative application of Bailey lemma ⓘ |
| namedAfter | W. N. Bailey ⓘ |
| 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
ⓘ
linked to:
Rogers–Ramanujan-type identities
Bailey lattice ⓘ Bailey lemma ⓘ Bailey transform ⓘ Göllnitz–Gordon identities ⓘ
linked to:
Rogers–Ramanujan-type identities
Rogers–Ramanujan identities ⓘ
linked to:
Rogers–Ramanujan-type identities
Rogers–Ramanujan-type identities ⓘ |
| 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 ⓘ
linked to:
Pochhammer symbol
q-difference equations ⓘ |
| yearIntroducedApprox | 1970s ⓘ |
How these facts were elicited
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Instruction
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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.