The conjecture of van der Waerden, which states that the permanent of a doubly stochastic matrix is at least $n^{-n} n!$.

The conjecture of van der Waerden, which states that the permanent of a doubly stochastic matrix is at least $n^{-n} n!$.

Proved by Gyires [Gy80], Egorychev [Eg81], and Falikman [Fa81].

[Gy80] Gyires, B., The common source of several inequalities concerning doubly stochastic matrices. Publ. Math. Debrecen (1980), 291-304. [Eg81] Egorychev, G. P., The solution of the van der Waerden problem for permanents. Dokl. Akad. Nauk SSSR (1981), 1041-1044. [Fa81] Falikman, D. I., Proof of the van der Waerden conjecture on the permanent of a doubly stochastic matrix. Mat. Zametki (1981), 931-938, 957.