derangement number

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1: 26.13 Permutations: Cycle Notation

… ►See §26.8 for generating functions, recurrence relations, identities, and asymptotic approximations. … ►The derangement number, $d(n)$, is the number of elements of ${𝔖}_n$ with no fixed points: ►

26.13.4 $$d(n)=n!\sum _{j=0}^n{(-1)}^j\frac{1}{j!}=\lfloor \frac{n!+\mathrm{e}-2}{\mathrm{e}}\rfloor .$$

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Symbols:

$\mathrm{e}$: base of natural logarithm, $!$: factorial (as in $n!$), $\lfloor x\rfloor$: floor of $x$ , $j$: nonnegative integer, $n$: nonnegative integer and $d(n)$: derangement number

Permalink:

http://dlmf.nist.gov/26.13.E4

Encodings:

pMML, png, TeX

See also:

Annotations for §26.13 and Ch.26

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2: 26.15 Permutations: Matrix Notation

… ►The number of derangements of $n$ is the number of permutations with forbidden positions $B=\{(1,1),(2,2),\mathrm{\dots },(n,n)\}$. …

3: Bibliography Z

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The Dilogarithm Function in Geometry and Number Theory. In Number Theory and Related Topics (Bombay, 1988), R. Askey and others (Eds.), Tata Inst. Fund. Res. Stud. Math., Vol. 12, pp. 231–249.

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External Links:

MathReview (J. Browkin), ZentralBlatt

Referenced by:

§25.12(i).

Encodings:

BibTeX

►

A modified Bernoulli number. Nieuw Arch. Wisk. (4) 16 (1-2), pp. 63–72.

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External Links:

ISSN 0028-9825, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.16(iii).

Encodings:

BibTeX

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Weighted derangements and the linearization coefficients of orthogonal Sheffer polynomials. Proc. London Math. Soc. (3) 65 (1), pp. 1–22.

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External Links:

ISSN 0024-6115, Document, Link, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.18(v).

Encodings:

BibTeX

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