  F. Bergeron recently asked the intriguing question whether $\binom{b+c}{b}_q
-\binom{a+d}{d}_q$ has nonnegative coefficients as a polynomial in $q$,
whenever $a,b,c,d$ are positive integers, $a$ is the smallest, and $ad=bc$. We
conjecture that, in fact, this polynomial is also always unimodal, and
combinatorially show our conjecture for $a\le 3$ and any $b,c\ge 4$. The main
ingredient will be a novel (and rather technical) application of Zeilberger's
KOH theorem.
