Question

Number of unordered factorizations of a non-square-free positive integer

score 232 · Answer 1 · 2020-08-07 02:28:26

232

Views

Number of unordered factorizations of a non-square-free positive integer

Published on 07 Aug 2020 - 2:28

score 68 · Answer 2 · 2020-08-14 22:29:47

68

Views

What does it mean to evaluate the 'inputs' of the Bell polynomial?

Published on 14 Aug 2020 - 22:29

score 192 · Answer 3 · 2020-08-27 09:10:51

192

Views

Relation between Bell number and $F(n)$ the number of partitions of $[n]$ without singeton blocks

Published on 27 Aug 2020 - 9:10

score 201 · Answer 4 · 2020-09-13 15:22:31

201

Views

Constructing a bijection to show that the number of equivalence relations on a finite set is equal to the bell numbers.

Published on 13 Sep 2020 - 15:22

score 463 · Answer 5 · 2020-09-20 17:29:15

463

Views

How to prove that $B(n) < n!$ for all $n \geq 3$ where $B(n)$ is $n$-th Bell number

Published on 20 Sep 2020 - 17:29

score 1.1k · Answer 6 · 2020-09-20 21:08:16

1.1k

Views

$F(n)$ is number of ways to partition set of $n$ without singleton blocks. Prove that $B(n) = F(n) + F(n+1)$

Published on 20 Sep 2020 - 21:08

score 295 · Answer 7 · 2021-01-14 20:58:57

295

Views

How many different equivalence relations with exactly two different equivalence classes are there on a set with $n$ elements

Published on 14 Jan 2021 - 20:58

score 218 · Answer 8 · 2021-01-25 18:39:57

218

Views

Compact formula for the $n$th derivative of $f\left(\sqrt{x+1}\right)$?

Published on 25 Jan 2021 - 18:39

score 227 · Answer 9 · 2021-03-03 08:06:21

227

Views

prove for bell number using induction on n

Published on 03 Mar 2021 - 8:06

score 102 · Answer 10 · 2021-03-08 21:37:59

102

Views

Show that $\left| A_n \right| = \sum_{k=1}^{n} (-1)^k \binom{n}{k} B(n - k)$ where $B(n)$ is the nth Bell number.

Published on 08 Mar 2021 - 21:37

score 260 · Answer 11 · 2021-03-11 02:47:06

260

Views

Bell numbers and a card shuffle

Published on 11 Mar 2021 - 2:47

score 101 · Answer 12 · 2021-04-19 16:43:01

101

Views

Problem about counting partitions

Published on 19 Apr 2021 - 16:43

score 86 · Answer 13 · 2021-04-23 09:45:46

86

Views

Bell number, equivalent.

Published on 23 Apr 2021 - 9:45

score 82 · Answer 14 · 2021-06-28 07:37:02

82

Views

Reference request for recurrence relation of the complete Bell polynomials $B_n$

Published on 28 Jun 2021 - 7:37

score 157 · Answer 15 · 2021-10-21 13:30:46

157

Views

Confusion about a factor in a composition of series/Faa di Bruno formula

Published on 21 Oct 2021 - 13:30

List Question

Number of unordered factorizations of a non-square-free positive integer

What does it mean to evaluate the 'inputs' of the Bell polynomial?

Relation between Bell number and $F(n)$ the number of partitions of $[n]$ without singeton blocks

Constructing a bijection to show that the number of equivalence relations on a finite set is equal to the bell numbers.

How to prove that $B(n) < n!$ for all $n \geq 3$ where $B(n)$ is $n$-th Bell number

$F(n)$ is number of ways to partition set of $n$ without singleton blocks. Prove that $B(n) = F(n) + F(n+1)$

How many different equivalence relations with exactly two different equivalence classes are there on a set with $n$ elements

Compact formula for the $n$th derivative of $f\left(\sqrt{x+1}\right)$?

prove for bell number using induction on n

Show that $\left| A_n \right| = \sum_{k=1}^{n} (-1)^k \binom{n}{k} B(n - k)$ where $B(n)$ is the nth Bell number.

Bell numbers and a card shuffle

Problem about counting partitions

Bell number, equivalent.

Reference request for recurrence relation of the complete Bell polynomials $B_n$

Confusion about a factor in a composition of series/Faa di Bruno formula

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