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arXiv · 2401.01027

A composition method for neat formulas of chromatic symmetric functions

David G. L. Wang·James Z. F. Zhou
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Abstract

We develop a composition method to unearth positive $e_I$-expansions of chromatic symmetric functions $X_G$, where the subscript $I$ stands for compositions rather than integer partitions. Using this method, we derive positive and neat $e_I$-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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David G. L. Wang, James Z. F. Zhou. 2024-11-22. A composition method for neat formulas of chromatic symmetric functions. https://arxiv.org/abs/2401.01027

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