Research in Number Theory

, 5:25 | Cite as

Unimodal sequence generating functions arising from partition ranks

  • Kathrin BringmannEmail author
  • Chris Jennings-Shaffer


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.


Unimodal sequences Strongly unimodal sequences Partitions Overpartitions Unimodal ranks Partition ranks Dyson rank \(M_2\)-rank Asymptotics Modular forms Mock modular forms 

Mathematics Subject Classification

05A16 11F03 11P81 11P82 



We thank Amanda Folsom and Jeremy Lovejoy for bringing [11] to our attention. We also thank the anonymous referees for their helpful comments and pointing out various typos in an earlier version of this manuscript.


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Authors and Affiliations

  1. 1.Faculty of Mathematical and Natural Sciences, Mathematical InstituteUniversity of CologneCologneGermany

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