Steingrímsson's sorting conjecture for revstack and stack sort

Let

be the symmetric group on $n$ letters, let

denote the stack-sorting operator, and let

denote the revstack-sorting operator. For a nonnegative integer $t$, write

and

undefined

\left|{\pi\in\mathfrak{S}_n:\mathcal{S}^t(\pi)=\mathrm{id}}\right|\leq\left|{\pi\in\mathfrak{S}_n:\mathcal{T}^t(\pi)=\mathrm{id}}\right|,

$$where$$

is the identity permutation. Furthermore, this inequality is strict for all pairs $(n,t)$ satisfying $2<t<n-1$.

The conjecture compares the sorting power of ordinary stack sort with its reverse-input variant; it asserts that revstack sort sorts at least as many permutations after every number of passes, with strict improvement in the indicated range. Its resolution is not specified in the source.