Note on Doron Zeilberger's paper: $\left(\genfrac{}{}{0ex}{}{5}{2}\right)$ proofs that $\left(\genfrac{}{}{0ex}{}{n}{k}\right)\le \left(\genfrac{}{}{0ex}{}{n}{k+1}\right)$ if $k<n/2$

Abstract

We present yet another algebraic proof of the unimodality of the binomial coefficients.