Reinforcement Learning the Chromatic Symmetric Function
This work addresses a combinatorial problem in graph theory, but it appears incremental as it builds on existing concepts with a new computational approach.
The authors tackled the problem of counting coefficients in the chromatic symmetric function of unit interval graphs by proposing a conjectural formula derived from reinforcement learning, which identifies universal conditions for counting specific disjoint cycle-tuples called Eschers.
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.