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In combinatorial mathematics, the Bell polynomials, named in honor of Eric Temple Bell, are used in the study of set partitions. They are related to Stirling and Bell numbers. They also occur in many applications, such as in the Faà di Bruno's formula.

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rdf:type	yago:Abstraction100002137 yago:Function113783816 yago:MathematicalRelation113783581 yago:Polynomial105861855 yago:Relation100031921 yago:WikicatPolynomials
rdfs:label	Bell-Polynom (de) Polinomios de Bell (es) Bell polynomials (en) Polynôme de Bell (fr) Polinomi di Bell (it) ベル多項式 (ja) 벨 다항식 (ko) Полиномы Белла (ru) Поліноми Белла (uk)
rdfs:comment	In combinatorial mathematics, the Bell polynomials, named in honor of Eric Temple Bell, are used in the study of set partitions. They are related to Stirling and Bell numbers. They also occur in many applications, such as in the Faà di Bruno's formula. (en) Im mathematischen Teilgebiet der Kombinatorik bezeichnen die Bell-Polynome, benannt nach Eric Temple Bell, folgende dreieckige Anordnung von Polynomen , wobei die Summe über alle Sequenzen von nicht-negativen ganzen Zahlen gebildet wird, so dass und . Das Bell-Polynom ist ein Polynom in den Variablen . Seine Koeffizienten sind ganze Zahlen. (de) En mathématiques, et plus précisément en combinatoire, un polynôme de Bell, nommé ainsi d'après le mathématicienEric Temple Bell, est défini par: où la somme porte sur toutes les suites j1, j2, j3, …, jn−k+1 d'entiers naturels telles que : et (fr) En combinatoria, los polinomios de Bell, nombrados en honor de Eric Temple Bell, se utilizan en el estudio de las particiones establecidas. Están relacionados con los números de Stirling y con los números de Bell. También aparecen en muchas aplicaciones, como en la fórmula de Faà di Bruno. (es) 組合せ数学におけるベル多項式（ベルたこうしき、英: Bell polynomials）とは、の名に因む、次の多項式で与えられる三角形配列のことである。ただしこの和は、を満たすすべての非負整数の列 j1, j2, j3, …, jn−k+1 について取られている。 (ja) 벨 다항식(영어: Bell polynomial)은 조합론에서 (Eric Temple Bell)의 이름을 따서 명명된 다항식이다. 또한 벨(Bell) 다항식은 집합 분할 연구에 사용된다. 이것은 스털링 수 및 벨 수와 관련이 있다. 그리고 이것들은 또한 (Faà di Bruno)의 과 같은 많은 응용에서 언급된다. (ko) Nella matematica combinatoria, i polinomi di Bell, in onore del matematico scozzese Eric Temple Bell, sono una famiglia di polinomi utilizzati nello studio delle partizioni di un insieme. Sono connessi ai numeri di Stirling e di Bell, e compaiono in numerose applicazioni, come ad esempio nella formula di Faà di Bruno. (it) В математике, в частности в комбинаторике, полиномы Белла — это полиномы вида где сумма берётся по всем последовательностям j1, j2, j3, ..., jn−k+1 неотрицательных целых чисел таким, что и Полиномы Белла названы так в честь математика Э. Белла. (ru) У комбінаториці поліноми Белла, що названі на честь , використовуються для вивчення заданих розділів. Вони пов'язані з та Белла. Вони також зустрічаються у багатьох програмах, наприклад у формулі Фаа ді Бруно. (uk)
dcterms:subject	Enumerative combinatorics Polynomials
Wikipage page ID	572498 (xsd:integer)
Wikipage revision ID	1124321510 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Bell number Probability distribution Monomial Determinant Enumerative combinatorics Annals of Mathematics Cycle index Convolution Mathematica Mathematics SageMath Generating function transformation Elementary symmetric polynomial Generating functions Moment (mathematics) Logarithm Combinatorics Faà di Bruno's formula Power sum symmetric polynomial Cayley–Hamilton theorem Cumulant Eric Temple Bell Exponential formula Exponential function Exponential generating function Exponentiation Formal power series Partition of a set Recurrence relation Hermite polynomials Polynomials Abstract and Applied Analysis Lah number Binomial type Touchard polynomials Dover Publications Maple (software) Idempotence Triangular array Factorial Symmetric group Stirling numbers of the second kind Bell matrix Bell numbers Integer partition Stirling number of the first kind Stirling number of the second kind Stirling numbers
Link from a Wikipage to an external page	http://doc.sagemath.org/html/en/reference/combinat/sage/combinat/combinat.html%23sage.combinat.combinat.bell_polynomial http://vinar.vin.bg.ac.rs/bitstream/id/12791/4374.pdf http://www.maplesoft.com/support/help/Maple/view.aspx%3Fpath=BellB https://web.archive.org/web/20140502084205/https:/cs.uwaterloo.ca/journals/JIS/VOL15/Griffiths/griffiths20.html https://web.archive.org/web/20170601062056/https:/archive.org/details/Comtet_Louis_-_Advanced_Coatorics https://web.archive.org/web/20200309144314/http:/vinar.vin.bg.ac.rs/bitstream/id/12791/4374.pdf%7Carchive-date=2020-03-09%7Curl-status=live http://reference.wolfram.com/mathematica/ref/BellY.html http://www.cs.uwaterloo.ca/journals/JIS/VOL15/Griffiths/griffiths20.html https://archive.org/details/Comtet_Louis_-_Advanced_Coatorics
sameAs	Bell polynomials Bell polynomials Bell polynomials Bell polynomials Bell polynomials Bell polynomials Bell polynomials Bell polynomials Bell polynomials Bell polynomials Bell polynomials Bell polynomials Bell polynomials
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