A Broken Circuit Model for Chromatic Homology Theories

TL;DR

This paper introduces a new algebraic Morse theory-based framework to categorify Whitney's broken circuit theorem, providing a novel perspective on chromatic polynomial and symmetric function invariants.

Contribution

It presents a categorification of the broken circuit theorem using algebraic Morse theory and thin poset methods, advancing the understanding of chromatic invariants.

Findings

Categorification of Whitney's broken circuit theorem

Application to chromatic polynomial and symmetric function

New algebraic Morse theory approach

Abstract

Using the tools of algebraic Morse theory, and the thin poset approach to constructing homology theories, we give a categorification of Whitney's broken circuit theorem for the chromatic polynomial, and for Stanley's chromatic symmetric function.