Combinatorial invariance of Kazhdan–Lusztig polynomials

Resolves the full combinatorial invariance conjecture: isomorphic Bruhat intervals in arbitrary Coxeter systems have identical equal-parameter Kazhdan–Lusztig polynomials. Thus the abstract order of the interval determines the polynomial, even across different Coxeter systems. (Lean)

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Combinatorial invariance of Kazhdan–Lusztig polynomials

September 24, 2026 · source · cite as \cite{OAI:Combinatorial-Invariance-of-Kazhdan-Lusztig-Polynomials-September-24-2026}

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.

Result 168 · Combinatorics. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.