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math.CO — Combinatorics

A counterexample to ordering-independence for chromatic operators

Contributed by Darij Grinberg

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.

Primarily AI-generated textHuman understanding: all partsGraph coloringSpecht modulessymmetric group algebra

Sep 28, 2026PDF ↗View work →

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