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Unimodal sequence generating functions arising from partition ranks

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Abstract

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.

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Acknowledgements

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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  1. Faculty of Mathematical and Natural Sciences, Mathematical Institute, University of Cologne, Weyertal 86-90, 50931, Cologne, Germany

    Kathrin Bringmann & Chris Jennings-Shaffer

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  1. Kathrin Bringmann
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  2. Chris Jennings-Shaffer
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Correspondence to Kathrin Bringmann.

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The research of the first author is supported by the Alfried Krupp Prize for Young University Teachers of the Krupp foundation and the research leading to these results receives funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013) / ERC Grant Agreement n. 335220 - AQSER.

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Bringmann, K., Jennings-Shaffer, C. Unimodal sequence generating functions arising from partition ranks. Res. number theory 5, 25 (2019). https://doi.org/10.1007/s40993-019-0164-z

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