Multiplicative properties of the number of k-regular partitions
October 21, 1:55 — 2:45pm at LIT 368.
Earlier this year, Bessenrodt and Ono proved surprising multiplicative properties of the partition function. In this project, we deal with \(k\)-regular partitions. Extending the generating function for \(k\)-regular partitions multiplicatively to a function on \(k\)-regular partitions, we show that it takes its maximum at an explicitly described small number of partitions, and thus can be easily computed. The basis for this is an extension of a classical result of Lehmer, from which we prove an inequality for the number of \(k\)-regular partitions which seems not to have been noticed before.