{"id":"openai-math/Combinatorial-Invariance-of-Kazhdan-Lusztig-Polynomials","pdf":"https://github.com/openai/math/blob/main/preprints/Combinatorial-Invariance-of-Kazhdan-Lusztig-Polynomials-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Combinatorial-Invariance-of-Kazhdan-Lusztig-Polynomials-September-24-2026","tags":["combinatorics","coxeter-groups","representation-theory"],"score":0,"title":"Combinatorial invariance of Kazhdan–Lusztig polynomials","domain":"Combinatorics","family":"168","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CO","summary":"We prove that an isomorphism of Bruhat intervals in arbitrary Coxeter systems preserves their equal-parameter Kazhdan–Lusztig polynomials. This resolves the full combinatorial invariance conjecture positively.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":2,"published":"2026-09-24","reactions":{},"discussion":[{"url":"https://gilkalai.wordpress.com/2026/10/07/updates-sharing-ai-progress-on-mathematics-amazing-and-my-lecture-plans/#:~:text=says%20that%20isomorphic%20Bruhat%20intervals%20have%20the%20same%20equal-parameter%20Kazhdan%E2%80%93Lusztig%20polynomial","date":"2026-10-07","kind":"web","site":"Combinatorics and more","text":"says that isomorphic Bruhat intervals have the same equal-parameter Kazhdan–Lusztig polynomial, even when the intervals come from different Coxeter systems. Ramanujan graphs and higher-dimensional expanders. The subject of New Ramanujan Graphs! returns with a deterministic polynomial-time…","added":"2026-10-24","title":"Updates: Sharing AI progress on mathematics (amazing!); and my lecture plans"},{"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":"Combinatorial invariance of Kazhdan–Lusztig polynomials"}