# Proof of the Bessenrodt–Ono Inequality by Induction

@article{Heim2021ProofOT, title={Proof of the Bessenrodt–Ono Inequality by Induction}, author={Bernhard Heim and Markus Neuhauser}, journal={Research in Number Theory}, year={2021} }

In 2016 Bessenrodt–Ono discovered an inequality addressing additive and multiplicative properties of the partition function. Generalizations by several authors have been given; on partitions with rank in a given residue class by Hou–Jagadeesan and Males, on k-regular partitions by Beckwith–Bessenrodt, on k-colored partitions by Chern–Fu–Tang, and Heim–Neuhauser on their polynomization, and Dawsey–Masri on the Andrews spt-function. The proofs depend on non-trivial asymptotic formulas related to…

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