Combinatorics > Related Articles

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Contents 1 Parent topics 2 Subtopics 2.1 Elementary topics 2.2 Other topics in enumerative combinatorics 2.3 Other subtopics 3 Other related topics

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]

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. [e]

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]: Add brief definition or description
• Young tableau [r]: Add brief definition or description

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]