A note on the inverse eigenvalue problem for symmetric doubly stochastic matrices (Q967507)

\textit{S.-G. Hwang} and \textit{S.-S. Pyo} [ibid. 379, 77--83 (2004; Zbl 1040.15010)] had claimed as a proposition that a real \(n\)-tuple \(1\geq \lambda_2 \geq \cdots \geq \lambda_n\) such that \[ \frac{1}{n} +\frac{\lambda_2}{n(n-1)}+\frac{\lambda_3}{(n-1)(n-2)}+\ldots +\frac{\lambda_n}{2(1)}\geq 0 \] is the spectrum of a symmetric doubly stochastic matrix. In this note, the author points out by a counterexample that the proposition is wrong.