Systems of parameters and the Cohen–Macaulay property

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