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Stirling Numbers of Forests and Cycles
2013
Electronic Journal of Combinatorics
For a graph $G$ and a positive integer $k$, the graphical Stirling number $S(G,k)$ is the number of partitions of the vertex set of $G$ into $k$ non-empty independent sets. Equivalently it is the number of proper colorings of $G$ that use exactly $k$ colors, with two colorings identified if they differ only on the names of the colors. If $G$ is the empty graph on $n$ vertices then $S(G,k)$ reduces to $S(n,k)$, the familiar Stirling number of the second kind.In this note we first consider
doi:10.37236/3170
fatcat:dumts6dakneoxjrsvj4jiswkfm