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Longer titles found: Stirling numbers and exponential generating functions in symbolic combinatorics (view), Stirling numbers of the first kind (view), Stirling numbers of the second kind (view)

searching for Stirling number 16 found (49 total)

alternate case: stirling number

Stirling transform (389 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \left\{{\begin{matrix}n\\k\end{matrix}}\right\}} is the Stirling number of the second kind, which is the number of partitions of a set of size

50 (number) (206 words) [view diff] exact match in snippet view article

the sum of two non-zero square numbers in two distinct ways. 50 is a Stirling number of the first kind and a Narayana number. Look up fifty in Wiktionary

65 (number) (533 words) [view diff] exact match in snippet view article

terms 28, 37, 49 (it is the sum of the first two of these). 65 is a Stirling number of the second kind, the number of ways of dividing a set of six objects

Partition of a set (1,879 words) [view diff] exact match in snippet view article find links to article

partitions of an n-element set into exactly k (non-empty) parts is the Stirling number of the second kind S(n, k). The number of noncrossing partitions of

90 (number) (2,028 words) [view diff] exact match in snippet view article

periodically (when leading zeroes are moved to the end). The eighteenth Stirling number of the second kind S ( n , k ) {\displaystyle S(n,k)} is 90, from a

Bernoulli polynomials (4,328 words) [view diff] exact match in snippet view article find links to article

\left\{{\begin{matrix}n\\k\end{matrix}}\right\}=S(n,k)} denotes the Stirling number of the second kind. The above may be inverted to express the falling

Permutation (11,671 words) [view diff] exact match in snippet view article find links to article

The number of n-permutations with k disjoint cycles is the signless Stirling number of the first kind, denoted c ( n , k ) {\displaystyle c(n,k)} or [

Eulerian number (2,460 words) [view diff] exact match in snippet view article find links to article

(t-1)^{n-k}} where { n k } {\textstyle \left\{{n \atop k}\right\}} is the Stirling number of the second kind. The permutations of the multiset { 1 , 1 , 2 ,

Pairwise comparison (psychology) (1,733 words) [view diff] exact match in snippet view article

{\displaystyle \sum _{k=1}^{n}k!S_{2}(n,k),} where S2(n, k) is the Stirling number of the second kind. One important application of pairwise comparisons

Necklace (combinatorics) (1,111 words) [view diff] exact match in snippet view article

{n}{d}},k\right)\;,} where S ( n , k ) {\displaystyle S(n,k)} are the Stirling number of the second kind. N k ( n ) {\displaystyle N_{k}(n)} (sequence A054631

Error function (7,328 words) [view diff] exact match in snippet view article find links to article

\end{aligned}}} zn denotes the rising factorial, and s(n,k) denotes a signed Stirling number of the first kind. There also exists a representation by an infinite

400 (number) (5,332 words) [view diff] exact match in snippet view article

binomial coefficient ( 11 5 ) {\displaystyle {\tbinom {11}{5}}} , stirling number of the second kind { 9 7 } {\displaystyle \left\{{9 \atop 7}\right\}}

Finite topological space (2,613 words) [view diff] exact match in snippet view article find links to article

{\displaystyle T(n)=\sum _{k=0}^{n}S(n,k)\,T_{0}(k)} where S(n,k) denotes the Stirling number of the second kind. Finite geometry Finite metric space Topological

Hyperharmonic number (1,095 words) [view diff] exact match in snippet view article find links to article

where [ n r ] r {\displaystyle \left[{n \atop r}\right]_{r}} is an r-Stirling number of the first kind. The above expression with binomial coefficients

Henry W. Gould (2,116 words) [view diff] exact match in snippet view article find links to article

Vandermonde's convolution, Amer. Math. Monthly, 64(1957), 409–415. Stirling number representation problems, Proc. Amer. Math. Soc., 11(1960), 447–451

Partition algebra (2,851 words) [view diff] exact match in snippet view article find links to article

where { k ℓ } {\displaystyle \left\{{k \atop \ell }\right\}} is a Stirling number of the second kind, ( ℓ | λ | ) {\displaystyle {\binom {\ell }{|\lambda