Question

Given permutation $\alpha \in S_n$; cycles formed by sequence $1, \alpha, \cdots$, are either identical or disjoint.

score 175 · Answer 1 · 2020-09-25 02:43:11

175

Views

Given permutation $\alpha \in S_n$; cycles formed by sequence $1, \alpha, \cdots$, are either identical or disjoint.

Published on 25 Sep 2020 - 2:43

score 239 · Answer 2 · 2020-10-06 11:06:59

239

Views

What is the smallest positive integer $m$ such that $g^m=e$ for all $g\in S_9$?

Published on 06 Oct 2020 - 11:06

score 152 · Answer 3 · 2020-10-09 02:39:03

152

Views

How many cycles are possible in an unlabeled complete graph?

Published on 09 Oct 2020 - 2:39

score 71 · Answer 4 · 2020-10-09 07:10:01

71

Views

Finding groups by the cycle decomposition of it's elements

Published on 09 Oct 2020 - 7:10

score 50 · Answer 5 · 2020-10-12 13:13:00

50

Views

Calculate the order of permutation of cycle compositions

Published on 12 Oct 2020 - 13:13

score 62 · Answer 6 · 2026-03-27 04:03:31

62

Views

Number of homomorphisms from $G = \langle x,y\mid x^{-1}yx=y^6\rangle$ to $S_5$

Published on 27 Mar 2026 - 4:03

score 68 · Answer 7 · 2020-10-13 09:20:44

68

Views

Understanding why the hint will prove that $A_{5}$ is generated by $3$-cycles.

Published on 13 Oct 2020 - 9:20

score 89 · Answer 8 · 2020-10-13 17:35:46

89

Views

Checking if this proof of $A_{5}$ is generated by $3$-cycles is a complete proof?

Published on 13 Oct 2020 - 17:35

score 47 · Answer 9 · 2020-10-14 12:43:03

47

Views

Proof that for any graph, each individual cycle cant be solved in less than n-1 swaps

Published on 14 Oct 2020 - 12:43

score 284 · Answer 10 · 2020-10-19 21:01:35

284

Views

Find all the permutations which commute with a given one

Published on 19 Oct 2020 - 21:01

score 39 · Answer 11 · 2020-10-20 20:50:59

39

Views

Am I setting up this proof correctly (show that the order of a cycle is equal to its length)?

Published on 20 Oct 2020 - 20:50

score 31 · Answer 12 · 2020-10-21 13:20:27

31

Views

Is there a formula or algorithm to find directly the isotropy groups of a permutation group acting on itself by conjugacy ??

Published on 21 Oct 2020 - 13:20

score 153 · Answer 13 · 2020-10-23 11:24:02

153

Views

Express a permutation as the product of two involutions

Published on 23 Oct 2020 - 11:24

score 1.1k · Answer 14 · 2020-10-23 14:49:07

1.1k

Views

Why are Stirling numbers of the first kind related to the number of permutations with $k$ cycles?

Published on 23 Oct 2020 - 14:49

score 58 · Answer 15 · 2020-10-24 21:01:40

58

Views

Show that $\sigma^2$ is a $p$-cycle when $p$ is odd, and $\sigma^2$ is not a cycle when $p$ is even with $p \neq 2$

Published on 24 Oct 2020 - 21:01

List Question

Given permutation $\alpha \in S_n$; cycles formed by sequence $1, \alpha, \cdots$, are either identical or disjoint.

What is the smallest positive integer $m$ such that $g^m=e$ for all $g\in S_9$?

How many cycles are possible in an unlabeled complete graph?

Finding groups by the cycle decomposition of it's elements

Calculate the order of permutation of cycle compositions

Number of homomorphisms from $G = \langle x,y\mid x^{-1}yx=y^6\rangle$ to $S_5$

Understanding why the hint will prove that $A_{5}$ is generated by $3$-cycles.

Checking if this proof of $A_{5}$ is generated by $3$-cycles is a complete proof?

Proof that for any graph, each individual cycle cant be solved in less than n-1 swaps

Find all the permutations which commute with a given one

Am I setting up this proof correctly (show that the order of a cycle is equal to its length)?

Is there a formula or algorithm to find directly the isotropy groups of a permutation group acting on itself by conjugacy ??

Express a permutation as the product of two involutions

Why are Stirling numbers of the first kind related to the number of permutations with $k$ cycles?

Show that $\sigma^2$ is a $p$-cycle when $p$ is odd, and $\sigma^2$ is not a cycle when $p$ is even with $p \neq 2$

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