Combinatorics/Related Articles

From Citizendium, the Citizens' Compendium
Jump to: navigation, search
This article is a stub and thus not approved.
Main Article
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
A list of Citizendium articles, and planned articles, about Combinatorics.
See also changes related to Combinatorics, or pages that link to Combinatorics or to this page or whose text contains "Combinatorics".

Parent topics

  • Mathematics [r]: The study of quantities, structures, their relations, and changes thereof. [e]
  • Discrete mathematics [r]: The disciplines within mathematics that study discrete objects: combinatorics, graph theory, number theory, mathematical logic, … [e]


Elementary topics

  • Binomial coefficient [r]: The number of possible choices of k elements out of n elements, disregarding order. [e]
  • Factorial [r]: The number of ways of arranging n labeled objects in order; the product of the first n integers. [e]
  • Generating function [r]: Function g(x,y) corresponding to a family of orthogonal polynomials ƒ0(x), ƒ1(x),…, where a Taylor series expansion of g(x,y) in powers of y will have the polynomial ƒn (x) as the coefficient for the term yn. [e]
  • Inclusion-exclusion principle [r]: Principle that, if A and B are finite sets, the number of elements in the union of A and B can be obtained by adding the number of elements in A to the number of elements in B, and then subtracting from this sum the number of elements in the intersection of A and B. [e]
  • Pigeonhole principle [r]: Principle, that if a very large set of elements is partitioned into a small number of blocks, then at least one block contains a rather large number of elements. [e]
  • Stirling number [r]: Coefficients which occur in the Stirling interpolation formula for a difference operator. [e]

Other topics in enumerative combinatorics

Other subtopics

Other related topics

  • Graph theory [r]: Field of mathematics studying graphs, which consist of nodes and arcs joining the nodes. [e]
  • Number theory [r]: The study of integers and relations between them. [e]