Banerjee, K., & Dastidar, M. G. (2022). Ramanujan’s Theta Functions and Parity of Parts and Cranks of Partitions. Annals of Combinatorics, 565–578. https://doi.org/10.1007/s00026-022-00615-1
E104-05 - Forschungsbereich Kombinatorik und Algorithmen
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Zeitschrift:
Annals of Combinatorics
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ISSN:
0218-0006
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Datum (veröffentlicht):
2022
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Umfang:
14
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Verlag:
SPRINGER BASEL AG
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Peer Reviewed:
Ja
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Keywords:
Cranks; Parity of parts; Partitions; Ramanujan’s theta functions
en
Abstract:
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.
