Sub(L)中的五边形格特征及其数量不等式

ON CHARACTERIGATION OF THE PENTAGON LATTICE IN Sub(L)AND ITS QUANTITATIVE INEGUALITY

五边形结构在刻画格的特征方面具有十分重要作用,应用格论及组合数学的方法讨论了格L与其子格格Sub(L)中所含五边形格之间的数量关系,给出了有限格L的子格格中三个元生成五边形格的充要条件,同时给出了Sub(L)所含不同五边形格数量的一个下界.

Many properties of a lattice can be characterized by the existence of some kind of pentagons.In this paper,the relationship between elements of a lattice and the number of pentagons of its sublattices are discussed based on the theory of lattice and combinatorial method.A sufficient and necessary condition on the forming of a pentagon by three elements in the sublattices-lattice of a finite lattice is given.At the same time,a lower bound of the different pentagon number of the sublattices-lattice contained in a finite lattice is provided.