The symmetric functions catalog

An overview of symmetric functions and related topics

2024-03-26

Kromatic symmetric functions

A $K$-theoretical analog of the chromatic symmetric functions were introduced in [CPS23], called the kromatic symmetric functions. These serves as a non-homogeneous lift of the chromatic symmetric functions introduced by Stanley [Sta95]. One main feature is that these expand positively into Grothendieck symmetric functions whenever the graph is a claw-free incomparability graph of a poset.

The kromatic symmetric functions are believed to distinguish all graphs, see [Pie24].

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