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.

Aliases (1)

Rogers–Ramanujan 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 identities NERFINISHED →
hasGeneralizationMethod	Andrews–Baxter–Forrester method NERFINISHED → Bailey chain method NERFINISHED → vertex operator method →
hasProperty	combinatorial → deep → modular → q-analytic →
namedAfter	Leonard James Rogers NERFINISHED → Srinivasa Ramanujan NERFINISHED →
relatedTo	Andrews–Gordon identities NERFINISHED → Bailey chains NERFINISHED → Bailey lemma NERFINISHED → Bailey pairs → Gordon identities NERFINISHED → Göllnitz–Gordon identities NERFINISHED → Schur identities NERFINISHED → Slater’s list of identities NERFINISHED → affine Lie algebras NERFINISHED → 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 (2)

Subject (surface form when different)	Predicate
Srinivasa Ramanujan ("Rogers–Ramanujan identities") →	notableWork
Dyson’s transform →	relatedTo