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Results tagged with co.combinatorics
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user 85967
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
8
votes
Accepted
Number of integer solutions of a linear equation under constraints
Proposition 1: The number of integer solutions of the equation
$$
\sum_{i=1}^{k}x_i = N
$$
where $x_i\geq n_i$ for $i=1,\ldots,k$, is given by
$$
{\small
\binom{N+k-1-n_1-n_2-...-n_k}{k-1}
…
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