William Keith

Affiliation: Michigan Technological University

Title Of Talk: On a conjecture of Andrews and Bachraoui

Abstract: Recently, Andrews and Bachraoui considered a generating function $F_{k,m}(q)$ associated with certain two-color partitions, and conjectured that this function has non-negative coefficients for $m=1$. They showed this property for $1 \leq k \leq 4$. With Kathrin Bringmann and Koustav Banerjee, the speaker showed that $F_{k,1}(q)$ has non-negative coefficients for $5 \leq k \leq 10$. Shane Chern has recently completed the proof of the original conjecture. This talk therefore focuses on a refined conjecture on the positivity of particular summands in the expression, which arose in the proof methods employed with Bringmann and Banerjee.

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