# On Chromatic Quasisymmetric Functions of Directed Graphs

@inproceedings{Ellzey2018OnCQ, title={On Chromatic Quasisymmetric Functions of Directed Graphs}, author={Brittney Ellzey}, year={2018} }

Chromatic quasisymmetric functions of labeled graphs were defined by Shareshian and Wachs as a refinement of Stanley's chromatic symmetric functions. In this extended abstract, we consider an extension of their definition from labeled graphs to directed graphs, suggested by Richard Stanley. We obtain an F-basis expansion of the chromatic quasisymmetric functions of all digraphs and a p-basis expansion for all symmetric chromatic quasisymmetric functions of digraphs, extending work of Shareshian… CONTINUE READING

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VIEW 1 EXCERPT

CITES BACKGROUND

## Chromatic Posets.

VIEW 1 EXCERPT

CITES BACKGROUND

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VIEW 3 EXCERPTS

CITES RESULTS, BACKGROUND & METHODS

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 16 REFERENCES

## Adv

VIEW 6 EXCERPTS

HIGHLY INFLUENTIAL

## Power Sum Expansion of Chromatic Quasisymmetric Functions

VIEW 9 EXCERPTS

HIGHLY INFLUENTIAL

## A Symmetric Function Generalization of the Chromatic Polynomial of a Graph

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## A second proof of the Shareshian--Wachs conjecture, by way of a new Hopf algebra

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## A modular relation for the chromatic symmetric functions of (3+1)-free posets

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Matrices

VIEW 2 EXCERPTS