Partition identities involving gaps and weights

Alladi, Krishnaswami

doi:10.1090/S0002-9947-97-01831-X

Partition identities involving gaps and weights
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Trans. Amer. Math. Soc. 349 (1997), 5001-5019 Request permission

Abstract:

We obtain interesting new identities connecting the famous partition functions of Euler, Gauss, Lebesgue, Rogers–Ramanujan and others by attaching weights to the gaps between parts. The weights are in general multiplicative. Some identities involve powers of 2 as weights and yield combinatorial information about some remarkable partition congruences modulo powers of 2.

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