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imported>Dmitrii Kouznetsov (New page: {{subpages}} '''Combinatoric''' is part of mathematics that deals with discrete combinations of some discrete objects. <!-- INSTRUCTIONS, DELETE AFTER READING: Related Articles page...) |
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==Parent topics== | |||
{{r|Mathematics}} | |||
{{r|Discrete mathematics}} | |||
==Subtopics== | |||
== | ===Elementary topics=== | ||
{{r| | {{r|Binomial coefficient}} | ||
{{r|Factorial}} | |||
{{r|Generating function}} | |||
{{r|Inclusion-exclusion principle}} | |||
{{r|Pigeonhole principle}} | |||
{{r|Stirling number}} | |||
===Other topics in enumerative combinatorics=== | |||
{{r|Cameron–Erdős conjecture}} | |||
{{r|Erdős–Fuchs theorem}} | |||
{{r|Latin square}} | |||
{{r|Umbral calculus}} | |||
===Other subtopics=== | |||
{{r|Algebraic combinatorics}} | |||
{{r| | {{r|Extremal combinatorics}} | ||
{{r| | {{r|Ramsey theory}} | ||
{{r|Young tableau}} | |||
==Other related topics== | ==Other related topics== | ||
{{r|Graph theory}} | |||
{{r|Number theory}} | |||
==Articles related by keyphrases (Bot populated)== | |||
Latest revision as of 16:01, 30 July 2024
- 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]
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(2N/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. [e]