T. Amdeberhan

Bergeron's conjecture&a tale of two binomial coefficients

Bergeron's conjecture states that, if $1\leq a<b<c<d$ are integers with $ad=bc$, then one has the coefficient-wise inequality ${\binom{b+c}b}_q \ge {\binom{a+d}a}_q$ among two Gaussian polynomials. It originated in algebraic combinatorics and is wide open. The corresponding inequality for binomial coefficients (i.e., t...