Touchard polynomial

English

Studied by Jacques Touchard.

Touchard polynomial (plural Touchard polynomials)

(mathematics) Any member of a polynomial sequence of binomial type defined by ${\\displaystyle T_{n}(x)=\\sum _{k=0}^{n}S(n,k)x^{k}=\\sum _{k=0}^{n}\\left\\{{n \\atop k}\\right\\}x^{k},}$ where ${\\displaystyle S(n,k)=\\left\\{{n \\atop k}\\right\\}}$ is a Stirling number of the second kind, i.e. the number of partitions of a set of size n into k disjoint non-empty subsets.

单词	Touchard polynomial
释义	Touchard polynomial English Etymology Studied by Jacques Touchard. Noun Touchard polynomial (plural Touchard polynomials) (mathematics) Any member of a polynomial sequence of binomial type defined by ${\\displaystyle T_{n}(x)=\\sum _{k=0}^{n}S(n,k)x^{k}=\\sum _{k=0}^{n}\\left\\{{n \\atop k}\\right\\}x^{k},}$ where ${\\displaystyle S(n,k)=\\left\\{{n \\atop k}\\right\\}}$ is a Stirling number of the second kind, i.e. the number of partitions of a set of size n into k disjoint non-empty subsets.
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