For w in the symmetric group S_n, let C_w be the corresponding modified, signless Kazhdan-Lusztig basis element of the type-A Hecke algebra H_n(q). An extension [Ann. Comb. 25, no. 3 (2021) pp. 757-787] of a result of Deodhar [Geom. Dedicata 36, (1990) pp. 95-119] implies that any factorization of the form f(q)C_w = C_v1 ... C_vr, with v1, . . . , vr maximal elements of parabolic subgroups of S_n and f(q) in N[q] depending on these, provides cancellation-free combinatorial interpretations of the polynomials (P_v,w(q) | v in S_n) appearing in the expansion of C_w in terms of the natural basis (T_v | v in S_n) of H_n(q). While the set of permutations w in S_n admitting such a factorization of C_w has not yet been characterized, we apply a result of Gaetz-Gao [Adv. Math. 457 (2024) Paper No. 109941] to describe a set for which such a factorization cannot exist.

翻译：对于对称群S_n中的元素w，设C_w为A型赫克代数H_n(q)中对应的修改后无符号Kazhdan-Lusztig基元素。Deodhar [Geom. Dedicata 36, (1990) pp. 95-119] 的一个结果的推广 [Ann. Comb. 25, no. 3 (2021) pp. 757-787] 表明，任何形如 f(q)C_w = C_v1 ... C_vr 的分解（其中 v1, . . . , vr 是S_n的抛物子群的极大元素，且f(q)属于依赖于这些元素的N[q]）都提供了将C_w按H_n(q)的自然基(T_v | v ∈ S_n)展开时出现的多项式(P_v,w(q) | v ∈ S_n)的无消去组合解释。尽管目前尚未完全刻画允许C_w具有此类分解的S_n中置换w的集合，我们应用Gaetz-Gao的结果[Adv. Math. 457 (2024) Paper No. 109941]来描述一个不可能存在此类分解的集合。