V2EX hasse diagram

Hasse Diagram

释义 Definition

哈斯图(Hasse diagram):用于表示偏序集(partially ordered set, poset)的图形。它通常只画出元素之间的覆盖关系(cover relation,即“刚好比它大/小一步”的关系),并省略由传递性可推得的连线,使结构更清晰。

发音 Pronunciation (IPA)

/hs darm/

例句 Examples

A Hasse diagram can help you see the order quickly.
哈斯图可以帮助你快速看清元素的大小规律。

In the Hasse diagram of this poset, we draw edges only for cover relations, so the transitive links are omitted.
在这个偏序集的哈斯图中,我们只为覆盖关系画连线,因此由传递性得到的连线会被省略。

词源 Etymology

Hasse diagram”以德国数学家 Helmut Hasse(赫尔穆特哈斯)命名。该图在序理论与格论中被广泛使用,用更简洁的方式呈现偏序关系的骨架结构(常可理解为偏序关系的“传递约简”所对应的图)。

相关词 Related Words

文学与名著用例 Literary Works

  • Introduction to Lattices and Order(B. A. Davey & H. A. Priestley)
  • Lattice Theory(Garrett Birkhoff)
  • Enumerative Combinatorics, Volume 1(Richard P. Stanley)
  • A Course in Combinatorics(J. H. van Lint & R. M. Wilson)
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