Question

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

score 233 · Answer 1 · 2026-03-25 22:10:57

233

Views

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

Published on 25 Mar 2026 - 22:10

score 69 · Answer 2 · 2026-03-25 19:06:11

69

Views

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

Published on 25 Mar 2026 - 19:06

score 193 · Answer 3 · 2026-03-26 01:23:36

193

Views

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

Published on 26 Mar 2026 - 1:23

score 202 · Answer 4 · 2026-03-25 23:42:33

202

Views

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

Published on 25 Mar 2026 - 23:42

score 464 · Answer 5 · 2026-03-25 22:05:13

464

Views

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

Published on 25 Mar 2026 - 22:05

score 1.1k · Answer 6 · 2026-03-25 19:07:09

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 25 Mar 2026 - 19:07

score 296 · Answer 7 · 2026-03-25 19:03:00

296

Views

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

Published on 25 Mar 2026 - 19:03

score 219 · Answer 8 · 2026-03-25 23:39:29

219

Views

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

Published on 25 Mar 2026 - 23:39

score 228 · Answer 9 · 2026-03-25 19:00:28

228

Views

prove for bell number using induction on n

Published on 25 Mar 2026 - 19:00

score 103 · Answer 10 · 2026-03-25 23:42:48

103

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 25 Mar 2026 - 23:42

score 262 · Answer 11 · 2026-04-05 23:26:42

262

Views

Bell numbers and a card shuffle

Published on 05 Apr 2026 - 23:26

score 104 · Answer 12 · 2026-05-10 09:44:55

104

Views

Problem about counting partitions

Published on 10 May 2026 - 9:44

score 89 · Answer 13 · 2026-04-30 06:18:16

89

Views

Bell number, equivalent.

Published on 30 Apr 2026 - 6:18

score 83 · Answer 14 · 2026-03-25 19:02:11

83

Views

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

Published on 25 Mar 2026 - 19:02

score 158 · Answer 15 · 2026-03-25 19:04:49

158

Views

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

Published on 25 Mar 2026 - 19:04

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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