Hasse diagram

Hasse diagram
A diagram which represents a finite poset, in which nodes are elements of the poset and arrows represent the order relation between elements. Transitivity of the order relation is tacit, in other words, if and then no arrow is drawn from x to z, but if there is no distinct z between x and y (such that ) then an arrow is draw from x to y.

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  • Hasse diagram — In the mathematical discipline known as order theory, a Hasse diagram (pronEng|ˈhɑːsə HAHS uh ), named after Helmut Hasse (1898 ndash;1979)) is a simple picture of a finite partially ordered set, forming a drawing of the transitive reduction of… …   Wikipedia

  • Hasse — may refer to:People with the surname Hasse: * Peter Hasse (c. 1585–1640), German organist and composer * Johann Adolph Hasse (1699–1783), German composer * Henry Hasse (1913–1977), US writer of science fiction * Helmut Hasse (1898–1979), German… …   Wikipedia

  • Hasse-Diagramm — In der Mathematik ist ein Hasse Diagramm eine bestimmte graphische Darstellung endlicher halbgeordneter Mengen. Solche Diagramme wurden 1967 von dem Mathematiker Helmut Hasse eingeführt. Das Hasse Diagramm für eine Halbordnung ist ein gerichteter …   Deutsch Wikipedia

  • Diagram — Further information: Chart Sample flowchart representing the decision process to add a new article to Wikipedia. A diagram is a two dimensional geometric symbolic representation of information according to some visualization technique. Sometimes …   Wikipedia

  • Mathematical diagram — This article is about general diagrams in mathematics. For diagrams in the category theoretical sense, see Diagram (category theory). Euclid s Elements, ms. from Lüneburg, A.D. 1200 Mathematical diagrams are diagrams in the field of mathematics,… …   Wikipedia

  • Helmut Hasse — Infobox Scientist name=Helmut Hasse birth date = August 25 1898 death date = December 26 1979 field = MathematicsHelmut Hasse (IPA2|ˈhasə) (25 August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known… …   Wikipedia

  • Frattini subgroup — Hasse diagram of the lattice of subgroups of the dihedral group Dih4 In the 3 element layer are the maximal subgroups; their intersection (the F. s.) is the central element in the 5 element layer. So Dih4 has only one non generating element… …   Wikipedia

  • Complemented lattice — Hasse diagram of a complemented lattice A point and a line of the Fano plane are complements, when In the mathematical discipline of order theory, a complemented lattice is a bounded lattice in which every element a …   Wikipedia

  • Modular lattice — Hasse diagram of N5, the smallest non modular lattice. In the branch of mathematics called order theory, a modular lattice is a lattice that satisfies the following self dual condition: Modular law x ≤ b implies… …   Wikipedia

  • Hassediagramm — In der Mathematik ist ein Hasse Diagramm eine bestimmte graphische Darstellung halbgeordneter Mengen. Solche Diagramme wurden 1967 von dem Mathematiker Helmut Hasse eingeführt. Das Hasse Diagramm für eine Halbordnung ist ein gerichteter Graph,… …   Deutsch Wikipedia

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