Recursive formulae for the multiplicative partition function (Q1283425)
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scientific article; zbMATH DE number 1275575
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Recursive formulae for the multiplicative partition function |
scientific article; zbMATH DE number 1275575 |
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Recursive formulae for the multiplicative partition function (English)
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31 October 1999
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The identity \[ np(n)=\sum^n_{k=1} \sigma(k)p (n-k) \] is well-known. Using elementary means, the authors prove an analogous identity involving partitions of multi-partite numbers. They use this identity to correct some erroneous results given long ago by MacMahon. A couple of errors appear on the first page; for example, \((1,0)+(1,0)+ (1,0)\) should be \((1,0)+ (1,0)+(0,1)\); \(f(12)p(2,1)\) should be \(f(12)=p(2,1)\).
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recursive formulae
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multiplicative partition function
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identities
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partitions of multi-partite numbers
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