6 papers
Proof of a conjecture of Andrews and El Bachraoui on the parity of two-color partitions
Koustav Banerjee, Kathrin Bringmann
In this paper, we prove a conjecture of Andrews and El Bachraoui concerning the parity of certain two-color partitions. Precisely, we show that if the Fourier coefficient …
Proof of a conjecture of Andrews and Bachraoui on a Hecke sum
Koustav Banerjee, Kathrin Bringmann
In this paper, we prove a conjecture of Andrews and Bachraoui relating a generating function arising from two-color partitions (with odd smallest part and restrictions on the even…
On congruence conjectures of Andrews and Bachraoui
Koustav Banerjee, Kathrin Bringmann, Mohamed El Bachraoui
Andrews and the third author recently studied congruences for certain restricted two-color partitions. They made two conjectures for Ramanujan-type congruences and a vanishing iden…
Restricted Overpartitions and concave compositions: their modularity and asymptotics
Koustav Banerjee, Kathrin Bringmann, Atul Dixit
In this paper we study restricted overpartitions and concave compositions. In several cases the resulting generating functions involve simultaneously modular forms, mock theta func…
On a conjecture of Andrews and Bachraoui
Koustav Banerjee, Kathrin Bringmann, William J. Keith
Recently, Andrews and Bachraoui considered a generating function associated with certain two-color partitions, and conjectured that this function has non-negative coef…
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 TurÃ…