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
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author Banerjee, Koustav
Dastidar, Manosij Ghosh
author_facet Banerjee, Koustav
Dastidar, Manosij Ghosh
author_sort Banerjee, Koustav
collection PubMed
description 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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spelling pubmed-104625402023-08-30 Ramanujan’s Theta Functions and Parity of Parts and Cranks of Partitions Banerjee, Koustav Dastidar, Manosij Ghosh Ann Comb Article 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. Springer International Publishing 2022-10-25 2023 /pmc/articles/PMC10462540/ /pubmed/37649986 http://dx.doi.org/10.1007/s00026-022-00615-1 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Banerjee, Koustav
Dastidar, Manosij Ghosh
Ramanujan’s Theta Functions and Parity of Parts and Cranks of Partitions
title Ramanujan’s Theta Functions and Parity of Parts and Cranks of Partitions
title_full Ramanujan’s Theta Functions and Parity of Parts and Cranks of Partitions
title_fullStr Ramanujan’s Theta Functions and Parity of Parts and Cranks of Partitions
title_full_unstemmed Ramanujan’s Theta Functions and Parity of Parts and Cranks of Partitions
title_short Ramanujan’s Theta Functions and Parity of Parts and Cranks of Partitions
title_sort ramanujan’s theta functions and parity of parts and cranks of partitions
topic Article
url 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
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