Flip Combinatorial Invariance for Weyl-type flipclasses

Let a flipclass be a combinatorial object arising from a Bruhat interval, and call it a Weyl-type flipclass when it is of Weyl type.

Flip Combinatorial Invariance conjecture. Flip Combinatorial Invariance holds for flipclasses of Weyl type.

The conjecture is motivated by the Combinatorial Invariance Conjecture for Kazhdan–Lusztig polynomials and by the paper’s results for dihedral flipclasses and bounded-height Weyl-type flipclasses. Its unrestricted validity for all Weyl-type flipclasses remains open.