Okounkov's log-concavity conjecture for Littlewood–Richardson coefficients

Let $c_{\mu, \nu}^{\lambda}$ denote the Littlewood–Richardson coefficient associated to partitions $\lambda$, $\mu$, and $\nu$. For a partition $\alpha$ and a positive integer $N$, let $N\alpha$ denote the partition obtained by multiplying every part of $\alpha$ by $N$. Okounkov's log-concavity conjecture. Let $\lambda, \mu, \nu$ be three partitions. Then

$$c_{(N+1)\mu, (N+1)\nu}^{(N+1)\lambda} \cdot c_{(N-1)\mu, (N-1)\nu}^{(N-1)\lambda} \leq (c_{N\mu, N\nu}^{N\lambda})^2,$$

for every integer $N \geq 1$. This is a proposed log-concavity property for Littlewood–Richardson coefficients; the supplied source does not establish its general validity, and the paper's title indicates that counterexamples are constructed.