Analogues of Alder-Type Partition Inequalities for Fixed Perimeter Partitions

Abstract

In a 2016 paper, Straub proved an analogue to Euler's partition identity for partitions with fixed perimeter. Later, Fu and Tang provided a refinement and generalization of Straub's analogue to $d$-distinct partitions as well as a result related to the first Rogers-Ramanujan identity. Motivated by Alder-type partition identities and their generalizations, we build on work of Fu and Tang to establish generalized Alder-type partition inequalities in a fixed perimeter setting, and notably, a reverse Alder-type inequality.