Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Authors: Garvan, Frank G., Sarma, Rishabh
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212647
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts. Frank G. Garvan and Rishabh Sarma. SIGMA 20 (2024), 097, 14 pages

We give combinatorial interpretations of two residual cranks of overpartitions defined by Bringmann, Lovejoy, and Osburn in 2009, analogous to the crank of partitions given by Andrews and the first author in 1988. As a consequence, we give new versions of their definitions without adjusted weights....