We recall numerical criteria for Cohen–Macaulayness related to system of parameters and introduce monomial ideals of König type which include the edge ideals of König graphs. We show that a monomial ideal is of König type if and only if its corresponding residue class ring admits a system of parameters whose elements are of the form \(x_i-x_j\). This provides an algebraic characterization of König graphs. We use this special parameter systems for the study of the edge ideal of König graphs and the study of the order complex of a certain family of posets. Finally, for any simplicial complex \(\Delta \) we introduce a system of parameters for \(K[\Delta ]\) with a universal construction principle, independent of the base field and only dependent on the faces of \(\Delta \). This system of parameters is an efficient tool to test Cohen–Macaulayness of the Stanley–Reisner ring of a simplicial complex.

我们回想起与参数系统有关的Cohen–Macaulayness数值标准，并介绍了König类型的单项式理想，其中包括König图的边缘理想。我们证明，当且仅当其相应的残基类环允许参数系统的元素形式为\（x_i-x_j \）时，单项式理想才是König类型。这提供了König图的代数表征。我们使用这个特殊的参数系统来研究König图的边缘理想和研究某些波塞族的阶次复杂度。最后，对于任何单形复数\（\ Delta \），我们引入\（K [\ Delta] \）的参数系统具有通用的构造原理，独立于基本字段，并且仅取决于\（\ Delta \）的面。该参数系统是测试简单复数的Stanley-Reisner环的Cohen-Macaulayness的有效工具。