On the second order fluctuations for minimal difference partitions

Abstract

The class of minimal difference partitions MDP(q) is defined by the condition that successive parts in an integer partition differ from one another by at least q≥0. As an extension, Bogachev and Yakubovich (2020) introduced a variable MDP-type condition encoded by an integer sequence q→=qi and found the limit shape. Based on their work, we establish a central limit theorem for the fluctuations of parts around the limit shape near the edge.