Let m denote the number of quasielectrons (QEs) in a quantum Hall system containing N particles altogether. We show in several general cases that for systems containing m QEs in a single angular momentum shell above N − m Fermions in an incompressible quantum liquid (IQL) state having filling factor ν =¹/₃ that there always exists a configuration whose symmetric correlation function G is nonzero. This extends recent comparable results concerning the IQL state. As a consequence, one can obtain (explicitly) a configuration having a nonzero G for all N ≤ 8 particle systems containing any number of QEs. To establish our result, we construct a family of multi-graphs on N vertices satisfying certain restraints on the degrees of the vertices and possessing the property that whenever one computes the linear symmetrization of the graph monomial of any member of the family, the result is always nonzero. The nonzero linear symmetrization that is obtained in each case is in fact an example of what is called a relative semi-invariant of a (generic) binary form of degree N. Thus, in addition to providing new correlation functions for systems of interacting Fermions containing QEs, our construction is of potential interest from both the invariant and graph theoretic standpoints.

令m表示总共包含N个粒子的量子霍尔系统中的准电子（QE）数。我们表明在几个一般情况下，对于含系统米在一个单一的角动量壳上述QES ñ -米费米子在不可压缩的量子液体（IQL）状态具有填充因子ν = ¹ / ₃总是存在，其对称相关函数的结构G为非零。这扩展了有关IQL状态的近期可比较结果。结果，一个人可以（明确地）获得一个对于所有N而言具有非零G的配置≤8个包含任意数量QE的粒子系统。为了建立结果，我们在N个顶点上构造了一组多重图，这些顶点满足对顶点度的一定限制，并且具有以下性质：每当计算该家族任何成员的图形单项式的线性对称性时，结果是总是非零。实际上，在每种情况下获得的非零线性对称化实际上是度N的（通用）二进制形式的相对半不变的一个示例。因此，除了为包含QE的相互作用的费米子系统提供新的相关函数外，从不变和图论的角度来看，我们的构造都具有潜在的意义。