Meta-rotations and the Structure of Stable Matchings in the Student Project Allocation Problem

Abstract: We formally introduce and present the concept of meta-rotations as a tool for navigating the lattice of stable matchings in the Student Project Allocation problem with lecturer preferences over students (SPA-S). Building on the structural result that the set of stable matchings in any SPA-S instance forms a distributive lattice, we define meta-rotations for this setting and demonstrate how they compactly encode transitions between matchings. Our framework generalises the classical notion of rotations in bipartite settings and provides a systematic way to traverse the lattice, thereby enabling efficient enumeration of the set of stable matchings in any given SPA-S instance.