For an indifference graph G, we define a symmetric function of increasing spanning forests of G. We prove that this symmetric function satisfies certain linear relations, which are also satisfied by the chromatic quasisymmetric function and unicellular $\textrm {LLT}$ polynomials. As a consequence, we give a combinatorial interpretation of the coefficients of the $\textrm {LLT}$ polynomial in the elementary basis (up to a factor of a power of $(q-1)$ ), strengthening the description given in [4].

中文翻译：

---

增加森林的对称函数

对于无差异图G，我们定义了一个增加跨越森林的对称函数G. 我们证明了这个对称函数满足一定的线性关系，色准对称函数和单细胞函数也满足这些线性关系。 $\textrm {LLT}$ 多项式。因此，我们给出了系数的组合解释 $\textrm {LLT}$ 基本基础中的多项式（最多为 $(q-1)$ )，加强了[4]中给出的描述。