Equivalence conjecture for the Stanley depths of powers of the maximal ideal and squarefree Veronese ideals

Let $R=K[x_1,\cdots, x_n]$ be a polynomial ring in $n$ variables. Let $I_{n,d}$ be the squarefree Veronese ideal generated by all squarefree monomials of degree $d$, and let $\mathfrak{m}$ be the irrelevant maximal ideal in $R$. Stanley-depth equivalence conjecture. The formula

$$\operatorname{Sdepth}(\mathfrak{m}^s)=\left\lceil \frac{n}{s+1} \right\rceil$$

implies

$$\operatorname{Sdepth}(I_{n,d})=d-1+\left\lceil \frac{n-(d-1)}{d+1} \right\rceil$$

and vice versa, where $s$ is a positive integer. The conjecture concerns the equivalence of the conjectural Stanley-depth formulas for these two classes of monomial ideals; the supplied text gives no evidence of resolution.