# An analogue of chromatic bases and $p$-positivity of skew Schur $Q$-functions

## TL;DR

This paper explores the relationship between chromatic symmetric functions and Schur Q-functions, introduces natural bases, and investigates p-positivity of skew Schur Q-functions, proposing a conjecture supported by computational evidence.

## Contribution

It constructs natural bases of the algebra generated by Schur Q-functions using chromatic symmetric functions and proposes a conjecture on p-positivity of all ribbon Schur Q-functions.

## Key findings

- Identified a class of p-positive ribbon Schur Q-functions
- Constructed natural bases of the algebra mma using chromatic symmetric functions
- Supported the conjecture with computational evidence

## Abstract

We investigate chromatic symmetric functions in the relation to the algebra $\Gamma$ of symmetric functions generated by Schur $Q$-functions. We construct natural bases of $\Gamma$ in terms of chromatic symmetric functions. We also consider the $p$-positivity of skew Schur $Q$-functions and find a class of $p$-positive ribbon Schur $Q$-functions, making a conjecture that they are \emph{all}. We include many concrete computational results that support our conjecture.