A Broken Circuit Model for Chromatic Homology Theories
A diagram visualizing the proof of the main theorem.
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 Stanley’s chromatic symmetric function. As an application, we obtain bounds on the homological span for both homology theories.
Type
Publication
On arXiv
Alex Chandler
Krener Assistant Professor
My research interests include machine learning, algebraic combinatorics, categorification, graph theory, knot theory, low dimensional topology, topological combinatorics.