The number of plane partitions in a bounded box is well-studied and dates back to MacMahon, at the start of this paper by Sam Hopkins and Tri Lai, p9, they summarized current results on the enumerations of several classes of plane partitions, especially the enumeration of skewed plane partitions of any shape $\lambda/\mu$ whose largest entry is bounded by some $m$, for any Young diagram $\mu$ contained in $\lambda$.
My question: is there a similar enumeration for the skewed plane partition of shape $\lambda/\mu$ with only row fillings reversed, i.e. weakly increase in the row fillings but weakly decrease in the column fillings?
Using LGV lemma is one possible approach as in this paper, we can reflect the shape horizontally and get a shape which weakly decreases in both directions, but it's no longer a skew shape, machinery in the paper doesn't apply directly.
Unlike other nice symmetry classes, based on my computation of a few simple cases, this enumeration formula may not have a nice product formula consisting of only linear terms but rather has a higher order irreducible polynomial and other linear terms.I haven't found any reference to this kind of plane partition, any reference will be appreciated.
