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A question on the Stirling numbers

score 93 · Answer 1 · 2019-09-30 15:57:43

93

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A question on the Stirling numbers

Published on 30 Sep 2019 - 15:57

score 1.7k · Answer 2 · 2026-03-25 23:35:47

1.7k

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Understanding relation between Product and Summation Notation

Published on 25 Mar 2026 - 23:35

score 511 · Answer 3 · 2014-03-27 04:15:31

511

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$\Delta^d m^n =d! \sum_{k} \left[ m \atop k \right] { {k+n} \brace m + d}(-1)^{m+k}$ Is this a new formula?

Published on 27 Mar 2014 - 4:15

score 87 · Answer 4 · 2014-03-28 23:41:05

87

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Can this sum be shown to be zero? $\sum_k \left[ {m+1} \atop k \right]{ k+n \brace m}(-1)^{m+k} = 0$

Published on 28 Mar 2014 - 23:41

score 587 · Answer 5 · 2014-03-29 10:18:45

587

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Proof on a property of Stirling Numbers of the first kind

Published on 29 Mar 2014 - 10:18

score 307 · Answer 6 · 2014-04-16 01:36:40

307

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number of ways to split n distinguishable objects into k indistinct sets - allowing for sets with 0 objects

Published on 16 Apr 2014 - 1:36

score 477 · Answer 7 · 2014-04-17 16:15:23

477

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Stirling Numbers of the First Kind and $S_n$.

Published on 17 Apr 2014 - 16:15

score 470 · Answer 8 · 2014-04-18 19:48:29

470

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Burnside's Lemma and Stirling Numbers of the First Kind

Published on 18 Apr 2014 - 19:48

score 1.1k · Answer 9 · 2014-04-29 00:30:23

1.1k

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Nonattacking rooks on a triangular chessboard

Published on 29 Apr 2014 - 0:30

score 419 · Answer 10 · 2014-05-11 20:32:42

419

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How do I show the following identify where c(n , k) represent unsigned stirling numbers of the first kind?

Published on 11 May 2014 - 20:32

score 1k · Answer 11 · 2014-05-22 17:01:15

1k

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Stirling Number of the Second Kind (intuition for formula)

Published on 22 May 2014 - 17:01

score 1.2k · Answer 12 · 2014-05-24 11:59:50

1.2k

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Stirling number of the second kind recurrence relations

Published on 24 May 2014 - 11:59

score 511 · Answer 13 · 2014-06-18 10:12:40

511

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What is this notation, similar to the binomial coefficient?

Published on 18 Jun 2014 - 10:12

score 1.4k · Answer 14 · 2014-06-20 05:01:56

1.4k

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Closed form for the Stirling numbers of the second kind.

Published on 20 Jun 2014 - 5:01

score 229 · Answer 15 · 2026-03-26 04:33:21

229

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Stirling-like sum equal to zero when $k>n$

Published on 26 Mar 2026 - 4:33

List Question

A question on the Stirling numbers

Understanding relation between Product and Summation Notation

$\Delta^d m^n =d! \sum_{k} \left[ m \atop k \right] { {k+n} \brace m + d}(-1)^{m+k}$ Is this a new formula?

Can this sum be shown to be zero? $\sum_k \left[ {m+1} \atop k \right]{ k+n \brace m}(-1)^{m+k} = 0$

Proof on a property of Stirling Numbers of the first kind

number of ways to split n distinguishable objects into k indistinct sets - allowing for sets with 0 objects

Stirling Numbers of the First Kind and $S_n$.

Burnside's Lemma and Stirling Numbers of the First Kind

Nonattacking rooks on a triangular chessboard

How do I show the following identify where c(n , k) represent unsigned stirling numbers of the first kind?

Stirling Number of the Second Kind (intuition for formula)

Stirling number of the second kind recurrence relations

What is this notation, similar to the binomial coefficient?

Closed form for the Stirling numbers of the second kind.

Stirling-like sum equal to zero when $k>n$

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