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Overpartitions into distinct parts

Moussa Ahmia and Mohammed L. Nadji
Vol. 14 (2025), No. 1, 65–74
DOI: 10.2140/cnt.2025.14.65
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.

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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
Authors
Moussa Ahmia
Department of Mathematics
University of Mohamed Seddik Ben Yahia
Jijel
Algeria		 LMAM Laboratory
Jijel
Algeria
Mohammed L. Nadji
Faculty of Mathematics
University of Science and Technology Houari Boumediene
Algiers
Algeria		 LMAM Laboratory
Jijel
Algeria		 RECITS Laboratory
Algiers
Algeria
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