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Claim. The site's commentary credits B. Gyires [Gy80], The common source of several inequalities concerning doubly stochastic matrices, with a proof of van der Waerden's conjecture: every doubly stochastic $n\times n$ matrix $X$ satisfies $\operatorname{per}(X)\ge n!/n^n$. By averaging the $n!$ diagonal products, that conjecture would give the statement of Problem 499. The paper does not prove the conjecture. Its Theorems 1.1–1.4 are inequalities for weighted sums of permanental quantities of $(AA^*)^{1/2}$, $(A^*A)^{1/2}$ and $A$, not bounds on $\operatorname{per}(A)$. On p. 293, van der Waerden's conjecture appears as a special case of the paper's own Conjectures 1.3 and 1.5. Corollaries 3.3 and 3.4 (pp. 299–300) give those conjectures for symmetric positive semidefinite matrices. Section 4 (p. 301) says the author could not prove them for arbitrary doubly stochastic matrices, beyond the cases $k=1,2$ of Conjecture 1.1 (Theorems 4.5 and 4.6). Theorem 4.9 and Corollary 4.1 (p. 304) give the bound only for the matrices $(1-x)A_0+xA$ with $0<x\le\delta$, where $A_0$ has every entry $1/n$. The paper ends by showing the conjecture equivalent to its Conjecture 4.1, which it leaves open. It proves no lower bound on the permanent of an arbitrary doubly stochastic matrix.

Why the attribution is rejected. The publication the site cites, Publ. Math. Debrecen 27 (1980), no. 3-4, 291–304, does not contain the theorem credited to it. Van der Waerden's conjecture was proved by Egorychev and Falikman, and the problem's statement by Marcus and Minc. The rejection concerns the attribution; the paper's own theorems are not in question.