It is known that unicellular LLT polynomials are related to the quasi-symmetric chromatic polynomials of certain graphs by the $(t-1)$-transform of symmetric functions. We investigate the extension of this transformation to various combinatorial Hopf algebras and prove a noncommutative version of this property.

中文翻译：

---

非可交换单细胞LLT多项式

众所周知，单细胞LLT多项式与某些图的拟对称色多项式有关 $（Ť-\mathrm{1个}）$-对称函数的变换。我们研究了这种变换对各种组合Hopf代数的扩展，并证明了该性质的非可交换形式。