A Broken Circuit Model for Chromatic Homology Theories

A diagram visualizing the proof of the main theorem.


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 Stanley’s chromatic symmetric function. As an application, we obtain bounds on the homological span for both homology theories.

On arXiv
Alex Chandler
Alex Chandler
Krener Assistant Professor

My research interests include machine learning, algebraic combinatorics, categorification, graph theory, knot theory, low dimensional topology, topological combinatorics.