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Maximal Multiplicative Properties of Partitions

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Abstract

Extending the partition function multiplicatively to a function on partitions, we show that it has a unique maximum at an explicitly given partition for any n ≠ 7. The basis for this is an inequality for the partition function which seems not to have been noticed before.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Leibniz University Hannover, Welfengarten 1, D-30167, Hannover, Germany

    Christine Bessenrodt

  2. Department of Mathematics and Computer Science, Emory University, Atlanta, GA, 30322, USA

    Ken Ono

Authors
  1. Christine Bessenrodt
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  2. Ken Ono
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Corresponding author

Correspondence to Ken Ono.

Additional information

The second author thanks the NSF and the Asa Griggs Candler Fund for their generous support.

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Bessenrodt, C., Ono, K. Maximal Multiplicative Properties of Partitions. Ann. Comb. 20, 59–64 (2016). https://doi.org/10.1007/s00026-015-0289-2

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  • DOI: https://doi.org/10.1007/s00026-015-0289-2

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