Permutation Cycle

Author

Eric W. Weisstein
December 16, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Combinatorics/PermutationCycle.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/PermutationCycle.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Usage

?FromCycles

?ToCycles

Examples

ToCycles[{4,2,1,3}]

ToCycles[{4,2,1,3}]

ToCycles[{5,3,4,2,6,1}]

Permutations[Range[3]]

ToCycles/@Permutations[Range[3]]

Counts

Table[PermutationCyclesD[2,n,k],{n,10},{k,n}]//TableForm

Collect[Series[Exp[-t u](1-t)^(-u),{t,0,8}],u]

Collect[1+Sum[AssociatedStirlingS1[n,k]t^n u^k/n!,{n,8},{k,n/2}],u]

Collect[1+Sum[AssociatedStirlingS1[n,k]t^n u^k/n!,{n,6},{k,n/2}],u]

Table[(-1)^(n-k)PermutationCyclesD[1,n,k],{n,8},{k,n}]//TableForm

Table[StirlingS1[n,k],{n,8},{k,n}]//TableForm

Table[PermutationCyclesD[4,n,k],{n,10},{k,n}]//TableForm

Select[Flatten[Table[PermutationCyclesD[1,n,k],{n,15},{k,n}]],#≠0&]

Select[Flatten[Table[PermutationCyclesD[2,n,k],{n,15},{k,n}]],#≠0&]

Select[Flatten[Table[PermutationCyclesD[3,n,k],{n,15},{k,n}]],#≠0&]

Select[Flatten[Table[PermutationCyclesD[4,n,k],{n,15},{k,n}]],#≠0&]

Select[Flatten[Table[PermutationCyclesD[5,n,k],{n,15},{k,n}]],#≠0&]