Combinatorial perspectives on identities for partitions with distinct even parts

Abstract

Partitions with distinct even parts have long been the subject of extensive research. In this paper, We present some new perspectives on such partitions from a combinatorial viewpoint, and connect them with signed partitions and bicolored partitions, thereby obtaining several partition identities. We construct bijective proofs for each of our results. Furthermore, these bijections will partially answer the combinatorial problems posed by Andrews-El Bachraoui and K$\imath$l$\imath$\c{c}-Kur\c{s}ung\"oz. respectively.