Hasse diagram

aka: concept lattice, poset, partially ordered set

Theory

• Automated Lattice Drawing ↗, 2004
• Yet a Faster Algorithm for Building the Hasse Diagram of a Concept Lattice ↗, 2009
• Lattice Drawing: Survey of Approaches, Geometric Method, and Existing Software ↗, 2009
• Border Algorithms for Computing Hasse Diagrams of Arbitrary Lattices ↗, 2011
• Confluent Hasse Diagrams ↗, 2018

References

• Hasse Diagrams of Integer Divisors ↗

Workaround

You can create a Hasse diagram manually, for example, using Graphviz diagram. The diagram above was created with the following code:

digraph hasse {
  bgcolor="transparent";
  node [shape=plaintext]
  edge [arrowhead=vee minlen=1];

  E[label="∅"]
  x[label="{x}"]
  y[label="{y}"]
  z[label="{z}"]
  xy[label="{x, y}"]
  yz[label="{y, z}"]
  xz[label="{x, z}"]
  xyz[label="{x, y, z}"]

  E -> x
  E -> y
  E -> z
  x -> xy
  y -> xy
  z -> yz
  x -> xz
  y -> yz
  z -> xz
  xy -> xyz
  xz -> xyz
  yz -> xyz

  x -> y -> z [style=invis minlen=5]
  xy -> xz -> yz [style=invis minlen=5]
  { rank=same; y x z }
  { rank=same; xy yz xz }
}