A MacMahon Analysis View of 4 Diagonal DSPPs

We study skew double-shifted plane partitions with three-element profiles using MacMahon's partition analysis. We present new generating function formulas for these partitions, incorporating an extra bound on the number of non-zero diagonal elements. These objects are closely related to the G\"ollnitz-Gordon and little G\"ollnitz identities. Moreover, we investigate some infinite hierarchies of $q$-series identities that stem from our formulas. We also observe certain palindromic properties within these generating functions. Finally, we examine these same objects from the perspective of linear partitions, which leads to interesting new $q$-series identities.