Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts
Year: 2024
Type: article
Abstract: 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. Furthermore, we investigate the combinatorial interpretation of an $M_2$-crank of partitions without repeated odd parts and explore connections of these statistics with their companion rank counterparts and the tenth order mock theta functions of Ramanujan.
Authors: Frank G. Garvan, Rishabh Sarma
Institution: University of Florida
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4403790781