{"id":"openai-math/Elementary-Positivity-of-Chromatic-Quasisymmetric-Functions","pdf":"https://github.com/openai/math/blob/main/preprints/Elementary-Positivity-of-Chromatic-Quasisymmetric-Functions-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Elementary-Positivity-of-Chromatic-Quasisymmetric-Functions-September-24-2026","tags":["algebraic-combinatorics","symmetric-functions","graph-theory"],"score":0,"title":"Elementary positivity of chromatic quasisymmetric functions","domain":"Combinatorics","family":"169","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CO","summary":"We prove that the chromatic quasisymmetric function of every natural unit interval graph is elementary-positive over $`\\mathbb N[q]`$. This resolves the elementary-positivity part of the Shareshian–Wachs conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":2,"published":"2026-09-24","reactions":{},"discussion":[{"url":"https://mathoverflow.net/a/482378","date":"2024-11-13","kind":"web","site":"mathoverflow.net","text":"Regarding question (1), I coded Hikita's (6) this evening. It checks out through $n \\leq 7$ and, for connected graphs, $n=8$ . Here's my Jupyter notebook , which I ran with SageMath 10.2.rc4. Personally I'm convinced. I don't see how Hikita's (6) could possibly fail for higher $n$ for this…","added":"2026-11-04","title":"Answer to: Status of the Stanley–Stembridge conjecture","author":"Joshua P. Swanson"},{"url":"https://mathoverflow.net/a/515897","date":"2026-10-10","kind":"web","site":"mathoverflow.net","text":"I'll remark on some problems in algebraic combinatorics. Combinatorial invariance of KL polynomials . Proved true, I'd say in agreement with the majority's sentiment. Shareshian--Wachs conjecture. Proved true, in line with nearly universal expectations. Saxl's conjecture. Proved true, in line with…","added":"2026-10-24","title":"Answer to: Which of the results released by OpenAI went against the conventional mathematical wisdom?","author":"Joshua P. Swanson"}],"formalized":false,"family_title":"Shareshian–Wachs elementary positivity"}