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- Hasse_diagram abstract "In order theory, a Hasse diagram (/ˈhæsə/; German: /ˈhasə/) is a type of mathematical diagram used to represent a finite partially ordered set, in the form of a drawing of its transitive reduction. Concretely, for a partially ordered set (S, ≤) one represents each element of S as a vertex in the plane and draws a line segment or curve that goes upward from x to y whenever y covers x (that is, whenever x < y and there is no z such that x < z < y). These curves may cross each other but must not touch any vertices other than their endpoints. Such a diagram, with labeled vertices, uniquely determines its partial order.Hasse diagrams are named after Helmut Hasse (1898–1979); according to Birkhoff (1948), they are so-called because of the effective use Hasse made of them. However, Hasse was not the first to use these diagrams; they appear, e.g., in Vogt (1895). Although Hasse diagrams were originally devised as a technique for making drawings of partially ordered sets by hand, they have more recently been created automatically using graph drawing techniques.The phrase "Hasse diagram" may also refer to the transitive reduction as an abstract directed acyclic graph, independently of any drawing of that graph, but this usage is eschewed here.".
- Hasse_diagram thumbnail Inclusion_ordering.svg?width=300.
- Hasse_diagram wikiPageExternalLink latdrawing.pdf.
- Hasse_diagram wikiPageExternalLink pbxglecx113c6axl.
- Hasse_diagram wikiPageID "338199".
- Hasse_diagram wikiPageRevisionID "567070178".
- Hasse_diagram hasPhotoCollection Hasse_diagram.
- Hasse_diagram title "Hasse Diagram".
- Hasse_diagram urlname "HasseDiagram".
- Hasse_diagram subject Category:Diagrams.
- Hasse_diagram subject Category:Graph_drawing.
- Hasse_diagram subject Category:Order_theory.
- Hasse_diagram type Artifact100021939.
- Hasse_diagram type Creation103129123.
- Hasse_diagram type Diagram103186399.
- Hasse_diagram type Diagrams.
- Hasse_diagram type Drawing103234306.
- Hasse_diagram type Object100002684.
- Hasse_diagram type PhysicalEntity100001930.
- Hasse_diagram type Representation104076846.
- Hasse_diagram type Whole100003553.
- Hasse_diagram comment "In order theory, a Hasse diagram (/ˈhæsə/; German: /ˈhasə/) is a type of mathematical diagram used to represent a finite partially ordered set, in the form of a drawing of its transitive reduction. Concretely, for a partially ordered set (S, ≤) one represents each element of S as a vertex in the plane and draws a line segment or curve that goes upward from x to y whenever y covers x (that is, whenever x < y and there is no z such that x < z < y).".
- Hasse_diagram label "Diagram Hassego".
- Hasse_diagram label "Diagrama de Hasse".
- Hasse_diagram label "Diagrama de Hasse".
- Hasse_diagram label "Diagramma di Hasse".
- Hasse_diagram label "Diagramme de Hasse".
- Hasse_diagram label "Hasse diagram".
- Hasse_diagram label "Hasse-Diagramm".
- Hasse_diagram label "Hasse-diagram".
- Hasse_diagram label "Диаграмма Хассе".
- Hasse_diagram label "ハッセ図".
- Hasse_diagram label "哈斯圖".
- Hasse_diagram sameAs Hasseův_diagram.
- Hasse_diagram sameAs Hasse-Diagramm.
- Hasse_diagram sameAs Diagrama_de_Hasse.
- Hasse_diagram sameAs Diagramme_de_Hasse.
- Hasse_diagram sameAs Diagramma_di_Hasse.
- Hasse_diagram sameAs ハッセ図.
- Hasse_diagram sameAs 하세_도형.
- Hasse_diagram sameAs Hasse-diagram.
- Hasse_diagram sameAs Diagram_Hassego.
- Hasse_diagram sameAs Diagrama_de_Hasse.
- Hasse_diagram sameAs m.01xrq3.
- Hasse_diagram sameAs Q901446.
- Hasse_diagram sameAs Q901446.
- Hasse_diagram sameAs Hasse_diagram.
- Hasse_diagram wasDerivedFrom Hasse_diagram?oldid=567070178.
- Hasse_diagram depiction Inclusion_ordering.svg.
- Hasse_diagram isPrimaryTopicOf Hasse_diagram.
