
In[]:=
matrix of the permutation (4 3 2)(1)
Input interpretation
matrix
(4 3 2) (1) (permutation)
Result
Show plot
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
Notations
Hide fixed points
Two-line notation

1
2
3
4
1
4
2
3

Permutation cycles
(2 4 3) (1)
One-line notation
1 4 2 3
Permutation rules
1  1
|
24
|
32
|
43
Basic properties
More
inverse
(2 3 4)
order
3
signature
1 (even)
index
2
Lexicographic properties
More
factoradic
0
4
2
3
0
2
0
1
longest increasing subsequence
1 4 2 3
increasing runs
1,4
2,3
lexicographic rank
th
5
permutation of 4 elements
Cycle structure
Show polygon graph
Show table
Cycle graph
Inversions
Show list
Inversion graph
Inversion vector
〈0, 1, 1〉
In[]:=
WolframAlpha["matrix of the permutation (4 3 2)(1)",{{"PermutationMatrix",1},"ComputableData"}]
Out[]=
Hold[{{1,0,0,0},{0,0,0,1},{0,1,0,0},{0,0,1,0}}]
In[]:=
ReleaseHold[Hold[{{1,0,0,0},{0,0,0,1},{0,1,0,0},{0,0,1,0}}]]
Out[]=
{{1,0,0,0},{0,0,0,1},{0,1,0,0},{0,0,1,0}}
In[]:=
MatrixForm[{{1,0,0,0},{0,0,0,1},{0,1,0,0},{0,0,1,0}}]
Out[]//MatrixForm=
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
In[]:=
MY[R_]:=Block[{A,B},A=%;B=A.R.A//MatrixForm;Return[B];]
In[]:=
MY
1
2
,0,0,-
1
2
,-
1
2
,1,0,-
1
2
,-
1
2
,0,1,-
1
2
,-
1
2
,0,0,
1
2

Out[]//MatrixForm=
Null.
1
2
,0,0,-
1
2
,-
1
2
,1,0,-
1
2
,-
1
2
,0,1,-
1
2
,-
1
2
,0,0,
1
2
.Transpose[Null]