Inclusion–exclusion principle

en

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Inclusion–exclusion principle

Quality:

Inclusion–exclusion principle - counting technique in combinatorics. Article “Inclusion–exclusion principle” in English Wikipedia has 54.8 points for quality (as of July 1, 2025). The article contains 20 references and 25 sections.

In this language version of Wikipedia the article has the best quality. Also, this article is the most popular in that (English) language version.

Since the creation of article “Inclusion–exclusion principle”, its content was written by 129 registered users of English Wikipedia and edited by 517 registered Wikipedia users in all languages.

The article is cited 94 times in English Wikipedia and cited 551 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #22007 in March 2005
  • Global: #20958 in April 2010

The highest popularity rank from 2008:

  • Local (English): #38817 in July 2017
  • Global: #60489 in July 2017

There are 30 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

Languages with the highest quality

#LanguageQuality gradeQuality score
1English (en)
Inclusion–exclusion principle
54.8146
2Vietnamese (vi)
Nguyên lý bao hàm-loại trừ
40.7858
3Serbian (sr)
Принцип укључења и искључења
37.0349
4Ukrainian (uk)
Формула включень-виключень
36.1395
5Russian (ru)
Формула включений-исключений
32.2714
6Chinese (zh)
排容原理
28.6349
7Galician (gl)
Principio de inclusión-exclusión
28.6182
8Persian (fa)
اصل شمول و عدم شمول
27.5034
9Slovenian (sl)
Načelo vključitev in izključitev
26.5975
10Catalan (ca)
Principi d'inclusió-exclusió
20.6348
More...

The following table shows the most popular language versions of the article.

Most popular in all the time

The most popular language versions of the article "Inclusion–exclusion principle" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Inclusion–exclusion principle
1 933 280
2German (de)
Prinzip von Inklusion und Exklusion
324 674
3Russian (ru)
Формула включений-исключений
321 392
4Spanish (es)
Principio de inclusión-exclusión
188 428
5Chinese (zh)
排容原理
183 110
6French (fr)
Principe d'inclusion-exclusion
179 245
7Polish (pl)
Zasada włączeń i wyłączeń
125 597
8Hebrew (he)
עקרון ההכלה וההפרדה
107 510
9Japanese (ja)
包除原理
86 835
10Persian (fa)
اصل شمول و عدم شمول
81 642
More...

The following table shows the language versions of the article with the highest popularity in the last month.

Most popular in June 2025

The most popular language versions of the article "Inclusion–exclusion principle" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Inclusion–exclusion principle
6 653
2Chinese (zh)
排容原理
963
3Russian (ru)
Формула включений-исключений
932
4German (de)
Prinzip von Inklusion und Exklusion
580
5Japanese (ja)
包除原理
531
6Spanish (es)
Principio de inclusión-exclusión
477
7French (fr)
Principe d'inclusion-exclusion
474
8Polish (pl)
Zasada włączeń i wyłączeń
462
9Persian (fa)
اصل شمول و عدم شمول
350
10Vietnamese (vi)
Nguyên lý bao hàm-loại trừ
306
More...

The following table shows the language versions of the article with the highest Authors’ Interest.

The highest AI

Language versions of the article "Inclusion–exclusion principle" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Inclusion–exclusion principle
129
2German (de)
Prinzip von Inklusion und Exklusion
62
3French (fr)
Principe d'inclusion-exclusion
56
4Italian (it)
Principio di inclusione-esclusione
36
5Russian (ru)
Формула включений-исключений
27
6Hebrew (he)
עקרון ההכלה וההפרדה
23
7Chinese (zh)
排容原理
19
8Polish (pl)
Zasada włączeń i wyłączeń
18
9Japanese (ja)
包除原理
16
10Persian (fa)
اصل شمول و عدم شمول
15
More...

The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

The highest AI in June 2025

Language versions of the article "Inclusion–exclusion principle" with the highest AI in June 2025
#LanguageAI awardRelative AI
1Russian (ru)
Формула включений-исключений
2
2Esperanto (eo)
Inkluziveco-ekskluda principo
1
3Slovak (sk)
Princíp zapojenia a vypojenia
1
4Serbian (sr)
Принцип укључења и искључења
1
5Catalan (ca)
Principi d'inclusió-exclusió
0
6Czech (cs)
Princip inkluze a exkluze
0
7German (de)
Prinzip von Inklusion und Exklusion
0
8English (en)
Inclusion–exclusion principle
0
9Spanish (es)
Principio de inclusión-exclusión
0
10Basque (eu)
Bilketa (probabilitatea)
0
More...

The following table shows the language versions of the article with the highest number of citations.

The highest CI

Language versions of the article "Inclusion–exclusion principle" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1Italian (it)
Principio di inclusione-esclusione
188
2English (en)
Inclusion–exclusion principle
94
3French (fr)
Principe d'inclusion-exclusion
35
4German (de)
Prinzip von Inklusion und Exklusion
30
5Spanish (es)
Principio de inclusión-exclusión
22
6Polish (pl)
Zasada włączeń i wyłączeń
22
7Russian (ru)
Формула включений-исключений
21
8Chinese (zh)
排容原理
18
9Hebrew (he)
עקרון ההכלה וההפרדה
16
10Japanese (ja)
包除原理
15
More...

Scores

Estimated value for Wikipedia:
English:
Global:
Popularity in June 2025:
English:
Global:
Popularity in all years:
English:
Global:
Authors in June 2025:
English:
Global:
Registered authors in all years:
English:
Global:
Citations:
English:
Global:

Quality measures

Interwikis

#LanguageValue
caCatalan
Principi d'inclusió-exclusió
csCzech
Princip inkluze a exkluze
deGerman
Prinzip von Inklusion und Exklusion
enEnglish
Inclusion–exclusion principle
eoEsperanto
Inkluziveco-ekskluda principo
esSpanish
Principio de inclusión-exclusión
euBasque
Bilketa (probabilitatea)
faPersian
اصل شمول و عدم شمول
fiFinnish
Seulaperiaate
frFrench
Principe d'inclusion-exclusion
glGalician
Principio de inclusión-exclusión
heHebrew
עקרון ההכלה וההפרדה
huHungarian
Szitaformula
hyArmenian
Կցման և արտաքսման սկզբունք
itItalian
Principio di inclusione-esclusione
jaJapanese
包除原理
koKorean
포함배제의 원리
nlDutch
Principe van inclusie en exclusie
plPolish
Zasada włączeń i wyłączeń
ptPortuguese
Princípio da inclusão-exclusão
ruRussian
Формула включений-исключений
skSlovak
Princíp zapojenia a vypojenia
slSlovenian
Načelo vključitev in izključitev
srSerbian
Принцип укључења и искључења
svSwedish
Principen om inklusion/exklusion
thThai
หลักการเพิ่มเข้าและตัดออก
ukUkrainian
Формула включень-виключень
urUrdu
اصول شمول استشنا
viVietnamese
Nguyên lý bao hàm-loại trừ
zhChinese
排容原理

Popularity rank trends

Best Rank English:
#38817
07.2017
Global:
#60489
07.2017

AI rank trends

Best Rank English:
#22007
03.2005
Global:
#20958
04.2010

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Inclusion–exclusion principle from Wikipedia articles about Derangement, Booles inequality, Cardinality, Subfactorial and De Morgans laws. Whereas reading the article about Inclusion–exclusion principle people most often go to Wikipedia articles on Booles inequality, Derangement, Combinatorics, Sieve theory and Cardinality.

Cumulative results of quality and popularity of the Wikipedia article

List of Wikipedia articles in different languages (starting with the most popular):

News from 26 September 2025

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In English Wikipedia the most popular articles on that day were: Google Chrome, Assata Shakur, James Comey, Voddie Baucham, They Call Him OG, Wounded Knee Massacre, Deaths in 2025, Ryder Cup, House of Guinness, Snake Eyes (1998 film).

About WikiRank

The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information