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The use of the chromatic polynomial of a graph in enumerative combinatorics. (English) Zbl 1313.05105

Summary: The chromatic polynomial of a graph on the set \(N=\{1,2,\dots,n\}\) is used as an instrument to find the number of possible partitions of \(N\) under some particular restraints and the number of functions on \(N\) with special properties.

MSC:

05C15 Coloring of graphs and hypergraphs
05C31 Graph polynomials
05C30 Enumeration in graph theory
11B73 Bell and Stirling numbers
05A15 Exact enumeration problems, generating functions
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