Question

Stirling Number of the First Kind: Recurrence relation

score 211 · Answer 1 · 2019-11-04 20:01:51

211

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Stirling Number of the First Kind: Recurrence relation

Published on 04 Nov 2019 - 20:01

score 101 · Answer 2 · 2019-11-04 20:44:45

101

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Stirling number of second kind and binomial coefficients, how to prove equality?

Published on 04 Nov 2019 - 20:44

score 126 · Answer 3 · 2019-11-05 17:25:13

126

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inequality for stirling numbers of second kind

Published on 05 Nov 2019 - 17:25

score 197 · Answer 4 · 2019-11-15 10:46:34

197

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Proof Stirling Numbers of First Kind

Published on 15 Nov 2019 - 10:46

score 65 · Answer 5 · 2026-03-26 14:43:00

65

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stirling number of the first kind

Published on 26 Mar 2026 - 14:43

score 584 · Answer 6 · 2019-11-24 01:58:14

584

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Stirling number second kind, $S(n, n-3) = \frac{n(n-1)(n-2)^2(n-3)^2}{48}$

Published on 24 Nov 2019 - 1:58

score 888 · Answer 7 · 2019-12-03 09:58:42

888

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How many equivalence relations on $\{a,b,c,d,e,f\}$ have $3$ equivalence classes?

Published on 03 Dec 2019 - 9:58

score 343 · Answer 8 · 2019-12-12 22:12:57

343

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Stirling numbers: Show that $S(n+1, r)=rS(n, r)+S(n, r-1)$.

Published on 12 Dec 2019 - 22:12

score 93 · Answer 9 · 2019-12-16 19:00:23

93

Views

I'm confused about the identity of Stirling numbers: $s(n,k) = k!S(n,k)$

Published on 16 Dec 2019 - 19:00

score 300 · Answer 10 · 2026-03-26 03:11:13

300

Views

Balls into Bins: probability that b bins have at least m balls

Published on 26 Mar 2026 - 3:11

score 118 · Answer 11 · 2019-12-18 07:47:03

118

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Prove that Stirling numbers satisfy the identity $\sum_{m} \binom {n}{m}S(m,k)S(n-m,l)= \binom{k + l}{l}S(n,k + l)$

Published on 18 Dec 2019 - 7:47

score 552 · Answer 12 · 2026-03-11 06:58:35

552

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Formula for computing the coefficients of Bell polynomial

Published on 11 Mar 2026 - 6:58

score 377 · Answer 13 · 2026-03-25 12:51:07

377

Views

generating function for Bell polynomial

Published on 25 Mar 2026 - 12:51

score 311 · Answer 14 · 2019-12-29 16:59:17

311

Views

Number of ways to partition a set with cardinality at least $k$ into $k$ nonempty subsets.

Published on 29 Dec 2019 - 16:59

score 78 · Answer 15 · 2020-01-07 00:13:07

78

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Asymptotic Expansion of MGF of squared Poisson - Touchard Polynomials and Second stirling number

Published on 07 Jan 2020 - 0:13

List Question

Stirling Number of the First Kind: Recurrence relation

Stirling number of second kind and binomial coefficients, how to prove equality?

inequality for stirling numbers of second kind

Proof Stirling Numbers of First Kind

stirling number of the first kind

Stirling number second kind, $S(n, n-3) = \frac{n(n-1)(n-2)^2(n-3)^2}{48}$

How many equivalence relations on $\{a,b,c,d,e,f\}$ have $3$ equivalence classes?

Stirling numbers: Show that $S(n+1, r)=rS(n, r)+S(n, r-1)$.

I'm confused about the identity of Stirling numbers: $s(n,k) = k!S(n,k)$

Balls into Bins: probability that b bins have at least m balls

Prove that Stirling numbers satisfy the identity $\sum_{m} \binom {n}{m}S(m,k)S(n-m,l)= \binom{k + l}{l}S(n,k + l)$

Formula for computing the coefficients of Bell polynomial

generating function for Bell polynomial

Number of ways to partition a set with cardinality at least $k$ into $k$ nonempty subsets.

Asymptotic Expansion of MGF of squared Poisson - Touchard Polynomials and Second stirling number

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