Abstract:In this work, we investigate the approach via flipclasses to the Combinatorial Invariance Conjecture for Kazhdan--Lusztig polynomials of all Coxeter groups. We prove the combinatorial invariance of Kazhdan--Lusztig $\widetilde{R}$-polynomials of Weyl groups modulo $q^7$ and of Kazhdan--Lusztig $\widetilde{R}$-polynomials of type $A$ Weyl groups modulo $q^8$. As a consequence, we establish the Combinatorial Invariance Conjecture for all intervals up to length 10 in Weyl groups and up to length 12 in type $A$ Weyl groups.
From: Mario Marietti [view email]
[v1]
Fri, 19 Sep 2025 21:17:25 UTC (29 KB)
[v2]
Thu, 17 Sep 2026 14:27:09 UTC (30 KB)
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