3 papers
math.NT2026
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…
math.CO2025
Combinatorial proof of a congruence for partitions into two sizes of part
Eli R. DeWitt, William J. Keith
Previous work showed that, for the number of partitions of into exactly two part sizes, one has . The earlier proof required the techn…
math.CO2025
Reciprocals of false theta functions
William J. Keith
We investigate reciprocals of false theta functions, producing results such as congruences, simple asymptotic bounds, and combinatorial identities. Of particular interest is a conn…