Reinforcement Learning the Chromatic Symmetric Function

TL;DR

This paper introduces a reinforcement learning approach to conjecturally compute coefficients of the chromatic symmetric function for unit interval graphs, revealing a universal counting formula based on specific graph structures.

Contribution

It presents a novel reinforcement learning method to identify a universal counting formula for chromatic symmetric function coefficients in unit interval graphs.

Findings

Reinforcement learning successfully identifies concatenation conditions for Escher cycles.

The proposed formula is conjectural but applies universally to all unit interval graphs.

The approach links graph theory with machine learning for combinatorial enumeration.

Abstract

We propose a conjectural counting formula for the coefficients of the chromatic symmetric function of unit interval graphs using reinforcement learning. The formula counts specific disjoint cycle-tuples in the graphs, referred to as Eschers, which satisfy certain concatenation conditions. These conditions are identified by a reinforcement learning model and are independent of the particular unit interval graph, resulting a universal counting expression.