Bergeron's conjecture & a tale of two binomial coefficients

Tewodros Amdeberhan, Matthias Beck

Bergeron's conjecture states that, if $1\le a<b<c<d$ are integers with $ad=bc$, then one has the coefficient-wise inequality ${\left(\genfrac{}{}{0ex}{}{b+c}{b}\right)}_q\ge {\left(\genfrac{}{}{0ex}{}{a+d}{a}\right)}_q$ among two Gaus…