# Combinatorics/Related Articles

From Citizendium, the Citizens' Compendium

*See also changes related to Combinatorics, or pages that link to Combinatorics or to this page or whose text contains "Combinatorics".*

## Contents

## 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, …
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## Subtopics

### 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.
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### Other topics in enumerative combinatorics

- Cameron–Erdős conjecture [r]: The number of sum-free sets contained in {1, 2, …,
*N*} is O(2^{N/2}).^{[e]} - Erdős–Fuchs theorem [r]: A statement about the number of ways that numbers can be represented as a sum of two elements of a given set.
^{[e]} - Latin square [r]:
*Add brief definition or description* - Umbral calculus [r]:
*Add brief definition or description*

### Other subtopics

- Algebraic combinatorics [r]:
*Add brief definition or description* - Extremal combinatorics [r]:
*Add brief definition or description* - Ramsey theory [r]: Branch of Graph theory which studies seemingly orderless systems and analyses the conditions under which order must be present.
^{[e]} - Young tableau [r]:
*Add brief definition or description*

- 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.
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