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Exponential formula

In combinatorial mathematics, the exponential formula (called the polymer expansion in physics) states that the exponential generating function for structures on finite sets is the exponential of the exponential generating function for connected structures. The exponential formula is a power series version of a special case of Faà di Bruno's formula.

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Algebraic statement

Combinatorial interpretation

Examples

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Exponential formula

Nodes35
Edges34
Triples9
Avg. degree1.94
Density0.057143
Components1

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Exponential formula

Top relations

related to Examples · 6
Exponential formula → Feynman, If, In, The, There, This
related to Other expressions · 2
Exponential formula → One, The
is a · 1
Exponential formula → power series version of a special case of Faà di Bruno's formula

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Important terminology

displaystyle connected formula exponential combinatorial set structures graphs also mathematics one numbers count number given power series algebraic statement see

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Exponential formulais apower series version of a special case of Faà di Bruno's formula0.90text
Exponential formularelated to ExamplesThis0.60section
Exponential formularelated to ExamplesIf0.60section
Exponential formularelated to ExamplesThere0.60section
Exponential formularelated to ExamplesIn0.60section
Exponential formularelated to ExamplesFeynman0.60section
Exponential formularelated to ExamplesThe0.60section
Exponential formularelated to Other expressionsOne0.60section
Exponential formularelated to Other expressionsThe0.60section

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