Hall-Littlewood functions, plane partitions, and the Rogers-Ramanujan identities. (English) Zbl 0707.05006
The author applies the theory of Hall-Littlewood functions to prove several multiple basic hypergeometric series identities, including some known generalizations of the Rogers-Ramanujan identities. The technique involves the partial fraction expansion of certain symmetric formal power series. The method also gives Proctor’s plane partition identities.
Reviewer: L.A.Székely
MSC:
| 05A19 | Combinatorial identities, bijective combinatorics |
| 05A17 | Combinatorial aspects of partitions of integers |
| 05A30 | \(q\)-calculus and related topics |
| 33C99 | Hypergeometric functions |
| 11P81 | Elementary theory of partitions |
Keywords:
hypergeometric series; plane partition; Rogers-Ramanujan identities; Hall-Littlewood functionsReferences:
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