Abstract

An overpartition of [Formula: see text] is a partition of [Formula: see text] in which the first occurrence of a number may be overlined. Then, the rank of an overpartition is defined as its largest part minus its number of parts. Let [Formula: see text] be the number of overpartitions of [Formula: see text] with rank congruent to [Formula: see text] modulo [Formula: see text]. In this paper, we study the rank differences of overpartitions [Formula: see text] for [Formula: see text] or [Formula: see text] and [Formula: see text]. Especially, we obtain some relations between the generating functions of the rank differences modulo [Formula: see text] and [Formula: see text] and some mock theta functions. Furthermore, we derive some equalities and inequalities on ranks of overpartitions modulo [Formula: see text] and [Formula: see text].

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.