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Combinations of Ranks and Cranks of Partitions Moduli 6, 9 and 12 and Their Comparison with the Partition Function

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Abstract

Let \(L \in \{6,9,12 \} \). We determine the generating functions of certain combinations of three ranks and three cranks modulo L in terms of eta quotients. Then, using the periodicity of signs of these eta quotients, we compare their values with the values of \(\frac{p(n)}{L/3}\).

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Acknowledgements

We thank the referee for the editorial suggestions which improved the article and pointing out additional conjectures which appear in Sect. 8.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB, T1K 3M4, Canada

    Zafer Selcuk Aygin

  2. Division of Mathematical Sciences School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Singapore

    Song Heng Chan

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  1. Zafer Selcuk Aygin
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  2. Song Heng Chan
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Correspondence to Zafer Selcuk Aygin.

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The authors are supported by the Singapore Ministry of Education Academic Research Fund, Tier 2, project number MOE2014-T2-1-051, ARC40/14.

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Aygin, Z.S., Chan, S.H. Combinations of Ranks and Cranks of Partitions Moduli 6, 9 and 12 and Their Comparison with the Partition Function. Ann. Comb. 23, 489–509 (2019). https://doi.org/10.1007/s00026-019-00468-1

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  • DOI: https://doi.org/10.1007/s00026-019-00468-1

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