Question

What's a formal definition of cycles that will allow me to prove this identity?

score 177 · Answer 1 · 2021-08-16 20:47:14

177

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What's a formal definition of cycles that will allow me to prove this identity?

Published on 16 Aug 2021 - 20:47

score 298 · Answer 2 · 2021-08-19 09:11:06

298

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Expected number of cycles for random permutation given that there are at least r cycles

Published on 19 Aug 2021 - 9:11

score 1k · Answer 3 · 2026-03-26 01:02:48

1k

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Fixed-Point Free Involutions

Published on 26 Mar 2026 - 1:02

score 72 · Answer 4 · 2021-09-06 12:22:50

72

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calculate $\left|C_{S_{12}}(\sigma)\right|$ whereas $\sigma=\left(1...6\right)\left(7...12\right)$

Published on 06 Sep 2021 - 12:22

score 38 · Answer 5 · 2021-09-08 19:37:47

38

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Prove that there exists at least one element $f$ in $S_4$ such that $f$ cannot be expressed as $g^4$ for any $g\in S_4$.

Published on 08 Sep 2021 - 19:37

score 118 · Answer 6 · 2021-09-17 18:16:30

118

Views

Suppose $n\geq 3$ and let $k$ be $n$ or $n-1$, whichever is odd. Show that the set of $k$-cycles in $A_n$ is not a conjugacy class in $A_n$.

Published on 17 Sep 2021 - 18:16

score 472 · Answer 7 · 2026-03-25 15:42:11

472

Views

Show that $S_n$ is a maximal subgroup of $S_{n+1}$.

Published on 25 Mar 2026 - 15:42

score 43 · Answer 8 · 2021-09-22 13:28:07

43

Views

Cycle index with characters inserted for the symmetric group

Published on 22 Sep 2021 - 13:28

score 52 · Answer 9 · 2021-09-24 12:43:38

52

Views

How do I find a specific group by its actions?

Published on 24 Sep 2021 - 12:43

score 37 · Answer 10 · 2021-09-26 16:10:25

37

Views

Identity permutation as a product of non-zero transpositions

Published on 26 Sep 2021 - 16:10

score 207 · Answer 11 · 2021-10-01 20:00:14

207

Views

how to determine the number of moved points of a commutator [g,h] from the shared moved points of g and h

Published on 01 Oct 2021 - 20:00

score 96 · Answer 12 · 2021-10-07 17:06:59

96

Views

Given 2 elements $x,y \in S_4$, is there any particular trick to determining the subgroup generated by them?

Published on 07 Oct 2021 - 17:06

score 58 · Answer 13 · 2021-10-08 18:46:52

58

Views

Cycle Index tables and a way to obtain $Z_m(S_p)$?

Published on 08 Oct 2021 - 18:46

score 271 · Answer 14 · 2021-10-09 05:36:58

271

Views

How to calculate a permutation to the $-100$th power?

Published on 09 Oct 2021 - 5:36

score 559 · Answer 15 · 2021-10-11 13:46:47

559

Views

Cycle notation and transpositions

Published on 11 Oct 2021 - 13:46

List Question

What's a formal definition of cycles that will allow me to prove this identity?

Expected number of cycles for random permutation given that there are at least r cycles

Fixed-Point Free Involutions

calculate $\left|C_{S_{12}}(\sigma)\right|$ whereas $\sigma=\left(1...6\right)\left(7...12\right)$

Prove that there exists at least one element $f$ in $S_4$ such that $f$ cannot be expressed as $g^4$ for any $g\in S_4$.

Suppose $n\geq 3$ and let $k$ be $n$ or $n-1$, whichever is odd. Show that the set of $k$-cycles in $A_n$ is not a conjugacy class in $A_n$.

Show that $S_n$ is a maximal subgroup of $S_{n+1}$.

Cycle index with characters inserted for the symmetric group

How do I find a specific group by its actions?

Identity permutation as a product of non-zero transpositions

how to determine the number of moved points of a commutator [g,h] from the shared moved points of g and h

Given 2 elements $x,y \in S_4$, is there any particular trick to determining the subgroup generated by them?

Cycle Index tables and a way to obtain $Z_m(S_p)$?

How to calculate a permutation to the $-100$th power?

Cycle notation and transpositions

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