Aval's oriented tree isomorphism conjecture

From papers

Let GG and HH be trees equipped with orientations γ\gamma. For an orientation γ\gamma, let χGγ(x;q)\chi_G^\gamma(x;q) denote the oriented chromatic quasisymmetric function obtained by weighting proper colorings according to the number of oriented ascents. Aval's oriented tree isomorphism conjecture. If GG and HH are non-isomorphic oriented trees, then

χGγ(x;q)χHγ(x;q).\chi_G^\gamma(x;q)\neq\chi_H^\gamma(x;q).

This generalizes the tree isomorphism conjecture to oriented chromatic quasisymmetric functions. The supplied text gives no resolution status for this oriented version, so it remains open in this record.

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Sources & referencesView supporting material

Primary source

Laura Colmenarejo and Ian Klein, “The Total Chromatic Quasisymmetric Functions of a Graph”, arXiv:2601.23170 (2026).

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