Maximal multiplicative properties of partitions

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 $n\neq 7$. The basis for this is an inequality for the partition function which seems not to have been noticed before.Comment: 5 pages; in replacement: one typo in References corrected. To appear in: Annals of Combinatoric