home about



Online Encyclopedia of
Mathematical Models.






Models:

boolean algebras, lattices, directed sets, equivalence relations,
graphs, directed graphs, bipartite graphs,
pre-orderings, strict partial orders, strict weak orderings, partial orderings, weak orderings, total orderings,
groups, rings, fields, racks, quandles, Tarski's HS Algebra,
more coming soon.



Equivalence Relations.
Relations

R 2-ary relation

Axioms

∀x xRx                            #reflexive

∀x∀y xRy ⟶ yRx                     #symmetric

∀x∀y∀z ((xRy ⋀ yRz) ⟶ xRz)       #transitive

Axioms

∀x xRx                            #reflexive

∀x∀y∀z ((xRz ⋀ yRz) ⟶ xRy)       #euclidean

Models
model 1_1
 R
  1
model 2_1
 R
  1 0
  0 1
model 2_2
 R
  1 1
  1 1
model 3_1
 R
  1 0 0
  0 1 0
  0 0 1
model 3_2
 R
  1 1 0
  1 1 0
  0 0 1
model 3_3
 R
  1 0 1
  0 1 0
  1 0 1
model 3_4
 R
  1 0 0
  0 1 1
  0 1 1
model 3_5
 R
  1 1 1
  1 1 1
  1 1 1
...more as textfile
      
Counts

oeis.org/A000110

oeis.org/A000041 up to isomorphism.

Comments

Models partitions of a set.

Generators

C code to enumerate all models, including isomorphsims. No search, just recursive enumeration




home about


Public domain. This website is still under construction.