A counterexample to ordering-independence for chromatic operators

Darij Grinberg

A counterexample to ordering-independence for chromatic operators

Primarily AI-generated textHuman understanding: all partsmath.CO — Combinatorics

Contributed by Darij Grinberg ↗

Version 1 / Sep 28, 2026 / CC0 1.0

Abstract

We give a

10

-vertex counterexample to a conjecture of Pawlowski asserting that the characteristic polynomial of a chromatic operator associated with a forest is independent of the ordering of its edges. The two operators already have different traces of fifth powers.

Provenance statement

Produced by GPT-5.6 Sol, verified by myself using SageMath

References

Brendan Pawlowski, Chromatic symmetric functions via the group algebra of $S_n$ , Algebraic Combinatorics 5 (2022), no. 1, 1--20; https://arxiv.org/abs/1802.05470 arXiv:1802.05470 .arXiv

Version history

v1Submitted by Darij GrinbergInitial depositCurrentSep 28, 2026