DOI: https://doi.org/10.14710/jfma.v8i1.24953

On the necessary and sufficient condition of a k-Euler pair

*Yosua Feri Wijaya orcid  -  Department of Mathematics, Universitas Gadjah Mada., Indonesia
Uha Isnaini orcid scopus  -  Department of Mathematics, Universitas Gadjah Mada., Indonesia
Yeni Susanti orcid scopus  -  Department of Mathematics, Universitas Gadjah Mada., Indonesia

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Abstract
In this paper, we discuss George Andrews’ definition of an Euler pair andSubbarao’s generalization of the Euler pair to a k-Euler pair. Let N and M be non-empty sets of natural numbers. A pair (N, M) is called a k-Euler pair if, for any natural number n, the number of partitions of n into parts from N is equal to the number of partitions of n into parts  from M, with  the  condition  that  each  part  appears  fewer than k times. We further explore several theorems concerning Euler pairs that were established by Andrews and Subbarao, and we present proofs using a method distinct from those previously utilized.
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Keywords: Partitions ; Number Theory ; Euler pair.
Funding: Indonesia Endowment Fund for Education (LPDP) under contract 202310210242421

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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