Raul Penaguiao
Published 2018-03-23, updated 2019-07-09Version 3
We study the chromatic symmetric function on graphs, and show that its kernel is spanned by the modular relations. We generalize this result to the chromatic quasisymmetric function on hypergraphic polytopes, a family of generalized permutahedra. We use this description of the kernel of the chromatic symmetric function to find other graph invariants that may help us tackle the tree conjecture.
Comments: 40 pages, 4 figures, this is the longer version
Chromatic quasisymmetric functions and noncommutative $P$-symmetric functions
A signed $e$-expansion of the chromatic symmetric function and some new $e$-positive graphs
On Calculating the Chromatic Symmetric Function
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