A new way of counting \(n^ m\) (Q1903757)
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scientific article; zbMATH DE number 825375
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new way of counting \(n^ m\) |
scientific article; zbMATH DE number 825375 |
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A new way of counting \(n^ m\) (English)
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1 February 1996
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This paper gives a combinatorial proof of the formula \[ n^m= \sum {m!\over k_1! k_2!\cdots k_{n- 1}!}, \] where \(m\) and \(n\) are positive integers, \(m\leq n\), and \(k_1, k_2,\dots, k_{n- 1}\) are nonnegative integers satisfying \(0\leq k_1+\cdots+ k_i\leq \min(i, m)\) for all \(i\).
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0.8545628
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0.8501212
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