Séminaire Lotharingien de Combinatoire, B42n (1999), 22 pp.

S. Ole Warnaar

Supernomial Coefficients, Bailey's Lemma and Rogers-Ramanujan-Type Identities. A Survey of Results and Open Problems

Abstract. 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 An-1 basic hypergeometric series, string functions and cylindric partitions.

Received: December 17, 1998; Accepted: May 10, 1999.

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