Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [permutation-cycles]

For elementary questions concerning permutation cycles and permutation groups. This includes all representations of permutations (two-line arrays, cycles, bipartite graphs); transpositions and the sign/parity of a permutation; the Symmetric group and the Alternating group. To be used with the (permutations) tag to make the distinction between abstract algebra permutation questions and combinatoric permutation questions.

For elementary questions concerning permutation cycles and permutation groups. This includes all representations of permutations (two-line arrays, cycles, bipartite graphs); transpositions and the sign/parity of a permutation; the Symmetric group and the Alternating group.

To be used with the to make the distinction between abstract algebra permutation questions and combinatoric permutation questions.

666 questions
0
votes
2 answers

How an order of permutation can be defined?

Let $\sigma$ be the permutation: [ \begin{array}{lllllllll} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ 3 & 5 & 6 & 2 & 4 & 9 & 8 & 7 & 1 \end{array} ] $I$ be the identity permutation and $m$ be the order of $\sigma$ i.e. $m=\min \left\{\text { positive…
user791345
0
votes
1 answer

Finding $\sigma^3$ and $\sigma^{-1}$ of non disjoint cycles

Let $\sigma=(257)(423)(57)(3416)\in S_8$ find $\sigma^3$ and $\sigma^{-1}$ So it is easier to calculate a product of disjoint cycles so we will first write the permutation as a product of disjoint cycle as any permeation can be written in this…
newhere
  • 3,115
0
votes
0 answers

Confusion on cycle notation

Let $\sigma \in S_4$ be the permutation that sends $(a,b,c,d) \to (b,d,a,c).$ Then the cycle notation is $(1342)=(23)(34)(12).$ But if we denote $a$ as $1,$ $b$ as $2$, $c$ as $3$ and $d$ as $4,$ then it means $\sigma(1)=2, \sigma(2)=4, \sigma(3)=…
Alexy Vincenzo
  • 5,400
0
votes
1 answer

Convert $(123)(456)(1457)$ into a disjoint cycle

I am struggling to solve this. According to $(123)$, $1$ gets sent to $2$, but according to $(456)(1457)$, $1$ gets sent to $5$. Can this be decomposed?
pinklemonade
  • 337
0
votes
1 answer

Permutation as string position recording in Wilson's FSG book

I'm reading Wilson's The Finite Simple Group book, mainly the Alternating group chapter, which explains the splitting criterion quite in detail. While heading there, I came across a possible permutation splitting in traspositions which Wilson…
riccardoventrella
  • 953
1
2