Ramanujan’s Theta Functions and Parity of Parts and Cranks of Partitions

In this paper, we explore intricate connections between Ramanujan’s theta functions and a class of partition functions defined by the nature of the parity of their parts. This consequently leads us to the parity analysis of the crank of a partition and its correlation with the number of partitions w...

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Detalles Bibliográficos
Autores principales: Banerjee, Koustav, Dastidar, Manosij Ghosh
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10462540/
https://www.ncbi.nlm.nih.gov/pubmed/37649986
http://dx.doi.org/10.1007/s00026-022-00615-1
Descripción
Sumario:In this paper, we explore intricate connections between Ramanujan’s theta functions and a class of partition functions defined by the nature of the parity of their parts. This consequently leads us to the parity analysis of the crank of a partition and its correlation with the number of partitions with odd number of parts, self-conjugate partitions, and also with Durfee squares and Frobenius symbols.

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