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Investigation of norms of overpartitions

Kumar, Abhimanyu (2023) Investigation of norms of overpartitions. Ramanujan Journal, 60 (1). pp. 181-193. ISSN 1382-4090. doi:10.1007/s11139-022-00637-6.

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For a partition, the norm is defined as the product of its parts. This paper aims to explore norms of overpartitions and develop their interpretations. The analysis begins by providing a two-variable generating function of the overline norm counting function r̅(i,n), which refers to the number of times i appears as a norm in the overpartitions of n. Thereafter, a wealth of intriguing relations like infinite series, integral representation, and recurrences are proved. Subsequently, an analogue of the multiplicative partition emerges, which is named the multiplicative overpartition function. Several curious results are unraveled on studying this function, which resemble the expressions involving the ordinary multiplicative partition function. The presented work opens a new avenue for research in norms and overpartitions.

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Kumar, Abhimanyu0000-0003-2966-9341
Additional Information:The author thanks the anonymous referee and the editor for their constructive comments which improved the presentation of this manuscript. This work was conducted while the author’s association with the Thapar Institute of Engineering and Technology, Patiala, Punjab 147004, India. This manuscript received no funding.
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Record Number:CaltechAUTHORS:20221017-15547800.33
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ID Code:117471
Deposited By: Research Services Depository
Deposited On:21 Oct 2022 20:11
Last Modified:25 Jan 2023 18:53

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