Resumen de On combinatorial invariance of parabolic Kazhdan–Lusztig polynomials

Grant T. Barkley, Christian Gaetz

• We show that the Combinatorial Invariance Conjecture for Kazhdan–Lusztig polynomials due to Lusztig and to Dyer, its parabolic analog due to Marietti, and a refined parabolic version that we introduce, are equivalent. We use this to give a new proof of Marietti’s conjecture in the case of lower Bruhat intervals and to prove several new cases of the parabolic conjectures.