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Abstract
In 2017, Byungchan, Choi, and Lovejoy investigated the overpartitions into distinct
parts without short sequences, where they established many combinatorial identities.
Our main goal is to explore the unrestricted case of the latter class, the overpartitions
into distinct parts, from a combinatorial point of view. In this vein, we establish
several identities related to the rank and crank of overpartitions into distinct parts.
Keywords
overpartition, distinct part, rank, crank
Mathematical Subject Classification
Primary: 11P81
Secondary: 05A15
Milestones
Received: 17 July 2024
Revised: 25 November 2024
Accepted: 10 December 2024
Published: 31 December 2024
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