{"id":"hexagon/2609.00118","pdf":"https://hexagonmath.org/pdf/2609.00118v1","url":"https://hexagonmath.org/abs/2609.00118v1","tags":["msc:05E05","msc:05C15","Graph coloring","Specht modules","symmetric group algebra"],"score":0,"title":"A counterexample to ordering-independence for chromatic operators","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Darij Grinberg"],"reviews":0,"subject":"math.CO","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-28","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"all"}