On new minimal excludants of overpartitions related to some $q$-series of Ramanujan

TL;DR

This paper introduces four new classes of minimal excludants for overpartitions, establishing their connections to Ramanujan's q-series functions, inspired by prior work on partition mex concepts.

Contribution

It defines novel minimal excludant classes for overpartitions and links them to Ramanujan's q-series, expanding the understanding of overpartition structures.

Findings

Four new minimal excludant classes for overpartitions introduced

Established relations between these excludants and Ramanujan's q-series functions

Extended the theory of minimal excludants in the context of overpartitions

Abstract

Inspired by Andrews' and Newman's work on the minimal excludant or "mex" of partitions, we define four new classes of minimal excludants for overpartitions and establish relations to certain functions due to Ramanujan.