3 papers
math.NT2026
A direct proof of Mono-Rolen-Stumpenhusen and new constructions via the Maass raising operators
Kathrin Bringmann, Ben Kane
In this paper, we give a direct conceptual proof of the main result of Mono, Rolen, and Stumpenhusen, using differential operators. More precisely, we realize their functions $ω_{k…
math.NT2025
Strict Log-concavity of -coloured Partitions
Kathrin Bringmann, Ben Kane, Anubhab Pahari +1
In recent years, there has been extensive work on inequalities among partition functions. In particular, Nicolas, and independently DeSalvo--Pak, proved that the partition function…
math.NT2025
A generic approach to proving Turán-type inequalities for sequences that admit exact formulas, with an application to unimodal sequences
Koustav Banerjee, Kathrin Bringmann, Ben Kane
We derive an asymptotic expansion with effective error bound for , counting the number of unimodal sequences of size . We prove that satisfies the higher order Turá…