Strict log-concavity conjecture for coefficients of non-equivariant motivic Chern classes

Let $p$ be a permutation and let $\mC[p]$ be its non-equivariant motivic Chern class, expanded in the Schubert basis $\{\mathbf{[w]}\}$. For each coefficient, write the resulting polynomial in $y$ as $\sum_{k=0}^d a_k y^k$; strict log-concavity means $a_k^2>a_{k-1}a_{k+1}$ for every $0<k<d$.

Strict log-concavity conjecture. The coefficients in the $\mathbf{[w]}$-expansion of the non-equivariant $\mC[p]$ classes are strictly log-concave.

Log-concavity is a proposed structural property of the coefficient polynomials in motivic Chern classes. The authors checked the conjecture for $n\leq 6$; no general proof or disproof is supplied.