On the restricted partition function |
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Authors: | Mircea Cimpoea? Florin Nicolae |
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Institution: | 1.Simion Stoilow Institute of Mathematics,Bucharest,Romania |
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Abstract: | For a vector \(\mathbf a = (a_1,\ldots ,a_r)\) of positive integers, we prove formulas for the restricted partition function \(p_{\mathbf a}(n): = \) the number of integer solutions \((x_1,\dots ,x_r)\) to \(\sum _{j=1}^r a_jx_j=n\) with \(x_1\ge 0, \ldots , x_r\ge 0\) and its polynomial part. |
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