Rogers–Ramanujan-type identities

E95684

mathematical concept partition identity q-series identity

Rogers–Ramanujan-type identities are a class of deep q-series and partition identities generalizing the classical Rogers–Ramanujan identities, with rich connections to combinatorics, number theory, and modular forms.

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All labels observed (7)

Label	Occurrences
Rogers–Ramanujan identities	2
Andrews–Gordon identities	1
Gordon identities	1
Göllnitz–Gordon identities	1
Rogers–Ramanujan type identities	1
Rogers–Ramanujan-type identities canonical	1
Schur identities	1

Statements (46)

Predicate	Object
instanceOf	mathematical concept ⓘ partition identity ⓘ q-series identity ⓘ
field	combinatorics ⓘ number theory ⓘ q-series ⓘ theory of modular forms ⓘ
generalizes	Rogers–Ramanujan-type identities self-linksurface differs ⓘ surface form: Rogers–Ramanujan identities
hasGeneralizationMethod	Andrews–Baxter–Forrester method ⓘ Bailey chain method ⓘ vertex operator method ⓘ
hasProperty	combinatorial ⓘ deep ⓘ modular ⓘ q-analytic ⓘ
namedAfter	Leonard James Rogers ⓘ Srinivasa Ramanujan ⓘ
relatedTo	Rogers–Ramanujan-type identities self-linksurface differs ⓘ surface form: Andrews–Gordon identities Bailey chains ⓘ Bailey lemma ⓘ Bailey pairs ⓘ Rogers–Ramanujan-type identities self-linksurface differs ⓘ surface form: Gordon identities Rogers–Ramanujan-type identities self-linksurface differs ⓘ surface form: Göllnitz–Gordon identities Rogers–Ramanujan-type identities self-linksurface differs ⓘ surface form: Schur identities Slater’s list of identities ⓘ affine Lie algebras ⓘ basic hypergeometric series ⓘ conformal field theory ⓘ generating functions ⓘ infinite product expansions ⓘ integer partitions with difference conditions ⓘ mock theta functions ⓘ modular equations ⓘ modular functions ⓘ modular invariance ⓘ partition theory ⓘ q-hypergeometric series ⓘ q-product expansions ⓘ representation theory ⓘ restricted partition functions ⓘ theta functions ⓘ vertex operator algebras ⓘ
usedIn	combinatorial bijections ⓘ proofs of partition congruences ⓘ q-series transformations ⓘ study of modular forms of half-integral weight ⓘ

Referenced by (8)

Full triples — surface form annotated when it differs from this entity's canonical label.

Dyson’s transform in number theory → relatedTo → Rogers–Ramanujan-type identities ⓘ

subject surface form: Dyson’s transform

Srinivasa Ramanujan → notableWork → Rogers–Ramanujan-type identities ⓘ

this entity surface form: Rogers–Ramanujan identities

Rogers–Ramanujan-type identities → generalizes → Rogers–Ramanujan-type identities self-linksurface differs ⓘ

this entity surface form: Rogers–Ramanujan identities

Rogers–Ramanujan-type identities → relatedTo → Rogers–Ramanujan-type identities self-linksurface differs ⓘ

this entity surface form: Andrews–Gordon identities

Rogers–Ramanujan-type identities → relatedTo → Rogers–Ramanujan-type identities self-linksurface differs ⓘ

this entity surface form: Göllnitz–Gordon identities

Rogers–Ramanujan-type identities → relatedTo → Rogers–Ramanujan-type identities self-linksurface differs ⓘ

this entity surface form: Gordon identities

Rogers–Ramanujan-type identities → relatedTo → Rogers–Ramanujan-type identities self-linksurface differs ⓘ

this entity surface form: Schur identities

Jacobi triple product → implies → Rogers–Ramanujan-type identities ⓘ

this entity surface form: Rogers–Ramanujan type identities