Maximal Multiplicative Properties of Partitions

By Christine Bessenrodt, Ken Ichi Ono. 2014

73 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/bbc6b52cd5152a7f13dcf8f80e4a080d22853798

How researchers see this paper

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In Algebra and Number Theory

1. Igor Pak
2. Stephen Desalvo

In Discrete Mathematics and Combinatorics

1. Igor Pak
2. Stephen Desalvo
3. Shelly Garion
4. Aner Shalev

Citations in the corpus

• Log-concavity of the partition function (2013, background): “n MathOver ow.2 After this paper was nished, we learned that it was also independently conjectured by Andrews and Hirschhorn.3 Most recently, a dierent but somewhat related investigation was made in [3]. 7.2. Historical background. The classical Hardy{Ramanujan formula is (21) p(n) = p 12 24n 1 XN k”