Stanley’s tree isomorphism conjecture

Determine whether chromatic symmetric functions distinguish all nonisomorphic trees; equivalently, prove that two trees with equal chromatic symmetric functions must be isomorphic.

Background

The paper places the tree-isomorphism problem among the major research directions related to chromatic symmetric functions. It states that Stanley asked whether chromatic symmetric functions distinguish trees and identifies this question as Stanley’s tree isomorphism conjecture, while noting that only several classes of trees are known to satisfy it.

References

In another direction Stanley asked whether chromatic symmetric functions distinguish trees, which is later called Stanley’s tree isomorphism conjecture.

— A quantitative way to e-positivity of trees  (2503.09484 - Li, 12 Mar 2025) in Section 1, Introduction, page 2