Hasse diagram

If (A,) is a finite poset, then it can be represented by a Hasse diagramMathworldPlanetmath, which is a graph whose vertices are elements of A and the edges correspond to the covering relation. More precisely an edge from xA to yA is present if

  • x<y.

  • There is no zA such that x<z and z<y. (There are no in-between elements.)

If x<y, then in y is drawn higher than x. Because of that, the direction of the edges is never indicated in a Hasse diagram.

Example: If A=𝒫({1,2,3}), the power setMathworldPlanetmath of {1,2,3}, and is the subset relationMathworldPlanetmath , then Hasse diagram is


Even though {3}<{1,2,3} (since {3}{1,2,3}), there is no edge directly between them because there are inbetween elements: {2,3} and {1,3}. However, there still remains an indirect path from {3} to {1,2,3}.

Title Hasse diagram
Canonical name HasseDiagram
Date of creation 2013-03-22 12:15:23
Last modified on 2013-03-22 12:15:23
Owner bbukh (348)
Last modified by bbukh (348)
Numerical id 18
Author bbukh (348)
Entry type Definition
Classification msc 05C90
Related topic Poset
Related topic PartialOrder