A composition method for neat formulas of chromatic symmetric functions
Abstract
We develop a composition method to unearth positive eI-expansions of chromatic symmetric functions XG, where the subscript I stands for compositions rather than integer partitions. Using this method, we derive positive and neat eI-expansions for the chromatic symmetric functions of tadpoles, barbells and generalized bulls, and establish the e-positivity of hats. We also obtain a compact ribbon Schur analog for the chromatic symmetric function of cycles.
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