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Dedekind’s \(\eta \)-function and Rogers-Ramanujan identities. (English) Zbl 1234.05040
Summary: We prove a \(q\)-series identity that generalizes Macdonald’s \(A_{2n}^{(2)} \eta \)-function identity and the Rogers-Ramanujan identities. We conjecture our result to generalize even further to also include the Andrews-Gordon identities.

MSC:
05A19 Combinatorial identities, bijective combinatorics
05E05 Symmetric functions and generalizations
11F20 Dedekind eta function, Dedekind sums
33D67 Basic hypergeometric functions associated with root systems
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