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Bell polynomials

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 Faà di Bruno's formula and an explicit formula for Lagrange inversion.

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Applications

Software

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Bell polynomials

Nodes58
Edges57
Triples42
Avg. degree1.97
Density0.034483
Components1

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Bell polynomials

Top relations

related to Symmetric polynomials · 6
Bell polynomials → Bell, Cayley, For, Hamilton, The, These
related to Faà di Bruno's formula · 5
Bell polynomials → Bell, Bruno's, Faà, Similarly, Suppose
related to Other identities · 5
Bell polynomials → Bell, Bigl, Bigr, Special, The
related to Software · 4
Bell polynomials → Bell, BellYMaple, IncompleteBellBSageMath, Mathematica
related to Derivatives · 3
Bell polynomials → Bell, Similarly, The
related to Generating functions · 3
Bell polynomials → Bell, In, The
related to Hermite polynomials · 3
Bell polynomials → Bell, Hermite, This
related to Reversion of series · 3
Bell polynomials → Bell, If, Let
related to Cycle index of symmetric groups · 2
Bell polynomials → Bell, The
related to Examples · 2
Bell polynomials → Bell, The

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Important terminology

bell polynomial polynomials displaystyle complete set given sum elements number also partitioned partial formula blocks thus partition bn partitions exponential

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Bell polynomialsrelated to Cycle index of symmetric groupsThe0.60section
Bell polynomialsrelated to Cycle index of symmetric groupsBell0.60section
Bell polynomialsrelated to DerivativesThe0.60section
Bell polynomialsrelated to DerivativesBell0.60section
Bell polynomialsrelated to DerivativesSimilarly0.60section
Bell polynomialsrelated to ExamplesThe0.60section
Bell polynomialsrelated to ExamplesBell0.60section
Bell polynomialsrelated to Exponential Bell polynomialsThe0.60section
Bell polynomialsrelated to Exponential Bell polynomialsBell0.60section
Bell polynomialsrelated to Faà di Bruno's formulaFaà0.60section
Bell polynomialsrelated to Faà di Bruno's formulaBruno's0.60section
Bell polynomialsrelated to Faà di Bruno's formulaBell0.60section

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