| 有限半模格的Hasse图 |
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| 引用本文： | 吕霞,唐高华,赵寿祥.有限半模格的Hasse图[J].广西师院学报,2014(2):4-9. |
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| 作者姓名： | 吕霞 唐高华 赵寿祥 |
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| 作者单位： | [1]广西师范学院数学科学学院,广西南宁530023 [2]桂林师范高等专科学校数学与计算机科学系,广西桂林541001 |
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| 基金项目： | 国家自然科学基金项目（11161006，11171142）；广西自然科学基金项目（2011GXNSFA018139）；广西“新世纪十百千人才工程”项目 |
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| 摘 要： | 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。
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| 关 键 词： | 格 格类 Hasse图 整数分拆 |
Hasse Diagrams of Some Finite Semimodular Lattices |
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| LV Xia,TANG Gao-hua,ZHAO Shou-xiang.Hasse Diagrams of Some Finite Semimodular Lattices[J].Journal of Guangxi Teachers College(Natural Science Edition),2014(2):4-9. |
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| Authors: | LV Xia TANG Gao-hua ZHAO Shou-xiang |
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| Institution: | 1. School of Mathematics Science, Guangxi Teachers Education University, Nanning 530023, China; 2.Department of Mathematics and Computer Sciences,Guilin Normal College, Guilin 541001, China) |
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| Abstract: | 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 . |
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| Keywords: | lattice class of a lattice Hasse diagram partition of an integer |
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