Séminaire Lotharingien de Combinatoire, B42n (1999), 22 pp.
S. Ole Warnaar
Bailey's Lemma and Rogers-Ramanujan-Type
Identities. A Survey of Results and Open Problems
An elementary introduction to the recently introduced A2 Bailey
lemma for supernomial coefficients is presented.
As illustration, some A2 q-series identities are (re)derived which
are natural analogues of the classical (A1) Rogers-Ramanujan identities
and their generalizations of Andrews and Bressoud.
The intimately related, but unsolved problems of supernomial inversion,
An-1 and higher level extensions are also discussed.
This yields new results and conjectures involving
hypergeometric series, string functions and cylindric partitions.
Received: December 17, 1998; Accepted: May 10, 1999.
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