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Some results on ordered and unordered fa...
Yaqubi, Daniel...

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Some results on ordered and unordered factorization of a positive integers by Yaqubi, Daniel ( Author )
Lemonjar Open Access
Australian National University
06-09-2023
As a well-known enumerative problem, the number of solutions of the equation $m=m_1+...+m_k$ with $m_1\leqslant...\leqslant m_k$ in positive integers is $\Pi(m,k)=\sum_{i=0}^k\Pi(m-k,i)$ and $\Pi$ is called the additive partition function. In this paper, we give a recursive formula for the so-called multiplicative partition function $\mu_1(m,k):=$ the number of solutions of the equation $m=m_1... m_k$ with $m_1\leqslant...\leqslant m_k$ in positive integers. In particular, using an elementary proof, we give an explicit formula for the cases $k=1,2,3,4$.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1412.0392
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