有限半模格的Hasse图

Hasse Diagrams of Some Finite Semimodular Lattices

主要是应用正整数的有序分拆,研究了有限格及其Hasse图问题,证明了有限格和有限格对应的Hasse图在同构意义下是一一对应的;引进了一个格的Hasse图的格类的概念,并给出了一种画n个顶点的格对应的Hasse图的简便而有效的方法,并且研究了有限半模格的Hasse图的一些性质.

In this paper ,we mainly study finite lattice and its Hasse diagram by using the parti-tion of a positive integer .We prove that the finite lattice and its corresponding Hasse diagram is one-to-one in the sense of isomorphism .We introduce the notion of class of a lattice and give a concise and effective way to draw a Hasse diagram of a lattice of n vertices .We also study some properties of Hasse diagrams of semimodular lattices .