Note on Doron Zeilberger's paper: ${5 \choose 2}$ proofs that ${n \choose k} \leq {n \choose {k+1}}$ if $k < n/2$

TL;DR

This paper offers an additional algebraic proof demonstrating the unimodality of binomial coefficients, reinforcing the understanding of their combinatorial properties.

Contribution

It introduces a new algebraic proof of binomial coefficient unimodality, expanding the set of known proofs and approaches.

Findings

Confirmed unimodality of binomial coefficients through algebraic methods

Provided a novel proof technique for a classical combinatorial property

Enhanced understanding of binomial coefficient inequalities

Abstract

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