On the necesarry and sufficient condition of a $k$-Euler pair

Yosua Feri Wijaya; Uha Isnaini; Yeni Susanti

doi:10.14710/jfma.v8i1.24953

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

On the necesarry and sufficient condition of a $k$-Euler pair

*Yosua Feri Wijaya

- Department of Mathematics, Universitas Gadjah Mada., Indonesia

Uha Isnaini

- Department of Mathematics, Universitas Gadjah Mada., Indonesia

Yeni Susanti

- Department of Mathematics, Universitas Gadjah Mada., Indonesia

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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Abstract

In this paper, we discuss George Andrews' definition of an Euler pair and Subbarao'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

In Vol 8, No 1 (2025)

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On the necesarry and sufficient condition of a $k$-Euler pair

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