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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.



Bipartite Graphs.
Axioms

relation       R(2)

relation       left(1)

variable       x,y

axiom              ∀x ¬ Rxx                     #antiReflexive

axiom              ∀x∀y Rxy ⟶ Ryx                     #symmetric

axiom              ∀x∀y Rxy ⟶ ¬(left x ⟷ left y)       #bipartite

Models
model 1_1
 R
   0
 left
   0
model 1_2
 R
   0
 left
   1
model 2_1
 R
   0 0
   0 0
 left
   0 0
model 2_2
 R
   0 0
   0 0
 left
   1 0
model 2_3
 R
   0 1
   1 0
 left
   1 0
model 2_4
 R
   0 0
   0 0
 left
   0 1
model 2_5
 R
   0 1
   1 0
 left
   0 1
model 2_6
 R
   0 0
   0 0
 left
   1 1
      



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