Generating all finite modular lattices of a given size

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• 作者：Peter Jipsen ; Nathan Lawless
• 关键词：Primary ; 06C05 ; Secondary ; 06C10 ; 05A15 ; modular lattices ; semimodular lattices ; counting up to isomorphism ; orderly algorithm
• 刊名：Algebra Universalis
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：74
• 期：3-4
• 页码：253-264
• 全文大小：563 KB
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• 作者单位：Peter Jipsen (1)
  Nathan Lawless (1)
  
  1. Chapman University, Orange, CA, United States
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8911

文摘

Modular lattices, introduced by R. Dedekind, are an important subvariety of lattices that includes all distributive lattices. Heitzig and Reinhold [8] developed an algorithm to enumerate, up to isomorphism, all finite lattices up to size 18. Here we adapt and improve this algorithm to construct and count modular lattices up to size 24, semimodular lattices up to size 22, and lattices of size 19. We also show that 2 n? is a lower bound for the number of nonisomorphic modular lattices of size n. Key words and phrases modular lattices semimodular lattices counting up to isomorphism orderly algorithm