Combinatorics

The two fundamental concepts in combinatorics are permutations and combinations.

A permutation is an arrangement of a set of objects, or specifically an arrangement of a subset of a certain size of some set of objects.

A combination is a subset of a certain size of some set of objects, without regard to their order.

These concepts are inherent to some kinds of probability problems.

For this reason Noether has always felt that studying combinatorics for its own sake is a bit like sex without love.

This is a starting point for anyone interested in the field of combinatorics. It's definitely one of my favorite facets of pure math, and I'll slowly be noding all the definitions. I've done some already, and I'll post a few a day untill I've noded everything on this list. In the meantime, I'll have added other hard-links, so I guess I'll never finish. But it's a start.

• abelian
• affine hull
• affine plane
• arborescence
• arrangement
• bell numbers
• binomial coefficient
• binomial theorem
• bipartite graph
• chain
• chromatic number
• clique
• code
• combination
• contraction
• convex
• convex hull
• Coxeter/Dynkin diagram
• Coxeter group
• Coxeter matrix
• cross polytope
• cycle
• Delaunay triangulation
• derangement
• design
• diameter
• difference set
• digraph
• division ring
• edge
• Eulerian graph
• Euler's formula
• Eulerian chain
• Eulerian cycle
• face
• Fary imbedding
• Fibonacci Sequence
• field
• finite difference
• flag
• flat
• forest
• four-color problem
• general position
• generating function
• girth
• graph
• group
• Hadamard matrix
• Hamiltonian chain
• Hamiltonian cycle
• hamming distance
• homeomorph
• hypercube
• hyperplane
• ideal
• inclusion/exclusion principle
• indegree
• independent set
• involution
• join
• Kirkman's Schoolgirls Problem
• latin square
• lattice
• laminated lattice
• magic square
• matroid
• medial axis
• Minkowski sum
• monoid
• nerve
• node
• orbit
• outdegree
• Pascal's formula
• Pascal's triangle
• path
• permutation
• Petersen graph
• pigeonhole principle
• planar graph
• planar straight line graph
• platonic solids
• polytope
• poset
• projective plane
• quaternion
• Ramsey's theorem
• recurrence relation
• regular polytope
• ring
• semigroup
• simplex
• simplicial complex
• site
• skeleton
• stable set
• Steiner triple systems
• Stirling number
• symmetric design
• system of distinct representatives
• tetrahedral numbers
• thrackle
• transitive
• tree
• triangular number
• triangulation
• Turan's theorem
• unimodality
• vertex
• Voronoi diagram
• wheel
• zero divisor
• zonotope
• Zorn's Lemma

• mathematics
• the math Project
• mathematics metanode
• Node More Mathematics
• nodes about math #1
  
  A full description of many combinatorical shapes can be found at georgehart.com as many of these defintions greatly benefit from a little graphical representation that defies ascii text.