About: Double counting (proof technique)

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In combinatorics, double counting, also called counting in two ways, is a combinatorial proof technique for showing that two expressions are equal by demonstrating that they are two ways of counting the size of one set. In this technique, which call "one of the most important tools in combinatorics", one describes a finite set from two perspectives leading to two distinct expressions for the size of the set. Since both expressions equal the size of the same set, they equal each other.

Attributes	Values
rdf:type	topical concept
rdfs:label	Double counting (proof technique) (en)
rdfs:comment	In combinatorics, double counting, also called counting in two ways, is a combinatorial proof technique for showing that two expressions are equal by demonstrating that they are two ways of counting the size of one set. In this technique, which call "one of the most important tools in combinatorics", one describes a finite set from two perspectives leading to two distinct expressions for the size of the set. Since both expressions equal the size of the same set, they equal each other. (en)
sameAs	Double counting (proof technique) Double counting (proof technique)
dbp:wikiPageUsesTemplate	dbt:= dbt:Citation dbt:Harvtxt dbt:Reflist dbt:Sfn dbt:Short_description
Subject	Articles containing proofs Mathematical proofs Enumerative combinatorics
thumbnail	wiki-commons:Special:FilePath/Cayley's_formula_2-4.svg?width=300
foaf:depiction
gold:hypernym	Technique
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Double_counting_(proof_technique)?oldid=1069819659&ns=0
Wikipage page ID	296942 (xsd:integer)
page length (characters) of wiki page	10526 (xsd:nonNegativeInteger)
Wikipage revision ID	1069819659 (xsd:integer)
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has abstract	In combinatorics, double counting, also called counting in two ways, is a combinatorial proof technique for showing that two expressions are equal by demonstrating that they are two ways of counting the size of one set. In this technique, which call "one of the most important tools in combinatorics", one describes a finite set from two perspectives leading to two distinct expressions for the size of the set. Since both expressions equal the size of the same set, they equal each other. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Double_counting_(proof_technique)
is Link from a Wikipage to another Wikipage of	Bijective proof Binomial coefficient Biregular graph Cayley's formula Double counting List of lemmas Combinatorial principles Combinatorial proof Hockey-stick identity Erdős–Gallai theorem Erdős–Ko–Rado theorem Handshaking lemma Fulkerson–Chen–Anstee theorem Lubell–Yamamoto–Meshalkin inequality Mathematical proof
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Double_counting_(proof_technique)

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