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].

## References

- [CPS23] Logan Crew, Oliver Pechenik and Sophie Spirkl. The kromatic symmetric function: a $k$-theoretic analogue of $x_g$. arXiv e-prints, 2023.
- [Pie24] Laura Pierson. Counting induced subgraphs with the Kromatic symmetric function. arXiv e-prints, 2024.
- [Sta95] Richard P. Stanley. A symmetric function generalization of the chromatic polynomial of a graph. Advances in Mathematics, 111(1):166–194, 1995.