The paper defines route operations that relate chromatic symmetric functions of graphs, proves forest graphs form a basis for symmetric functions by a combinatorial argument, and derives a subgraph-counting formula for the monomial-basis coefficients.
A weighted graph polynomial f rom chromatic invariants of knots
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On Calculating the Chromatic Symmetric Function
The paper defines route operations that relate chromatic symmetric functions of graphs, proves forest graphs form a basis for symmetric functions by a combinatorial argument, and derives a subgraph-counting formula for the monomial-basis coefficients.