Hasse diagram

A Hasse diagram is a graphical representation of a partially ordered set.

Misc.

 Subsets of a 2-element set Subsets of a 3-element set Divisors of 60 ordered by divisibility Non-negative integers ordered by divisibility Young–Fibonacci lattice Young's lattice Left: Divisors of 120 ordered by divisibility (Birkhoff's representation theorem) Associahedron of order 4 Permutohedron of order 4 Lattice of regular bands Free distributive lattices of monotonic Boolean functions Rieger–Nishimura lattice (free Heyting algebra over one generator) Types of quadriliterals

Tesseract

Subsets of a 4-element set:

 Emphasis on two cubes Rhombic dodecahedral parallel projection of the tesseract Logical connectives Emphasis on all eight cubes 4x4 matrix Tetrahedral central projection of the tesseract Not a Hasse diagram, but similar: Highest element in center; lower elements farer away from center; lowest element not shown

Set partitions

Partitions of a 4-element set ordered by refinement:

 Only the 14 noncrossing partitions (This diagram is also vertically symmetric.) Emphasis on sublattice Emphasis on symmetry Emphasis on number of elements per rank

First-order logic

v:Formulas in predicate logic

Root systems

 A7 C5 F4