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Results tagged with co.combinatorics
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user 27069
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
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answer
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Sum over integer compositions of $m$ with $n$ parts of a fixed monomial in the parts
Is there an explicit formula for the following quantity?
$$f_m(a_1,\ldots,a_n):=\sum_{\substack{k_1+\ldots+k_n=m \\ k_1,\ldots,k_n\in \mathbb{N}}} k_1^{a_1}\ldots k_n^{a_n}\ ,\hspace{1cm} m,a_1,\ldot …
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