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Unimodal sequence generating functions arising from partition ranks. (English) Zbl 1416.05016

Summary: In this paper we study generating functions resembling the rank of strongly unimodal sequences. We give combinatorial interpretations, identities in terms of mock modular forms, asymptotics, and a parity result. Our functions imitate a relation between the rank of strongly unimodal sequences and the rank of integer partitions.

MSC:

05A15 Exact enumeration problems, generating functions
05A16 Asymptotic enumeration
05A17 Combinatorial aspects of partitions of integers
11F03 Modular and automorphic functions
11P81 Elementary theory of partitions
11P82 Analytic theory of partitions
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