Shaun Culver
Aug17-08, 02:24 PM
I would like if there is a notion similar to that of a "power set" where the order of the elements in a set is accounted for - the elements are permuted, and each arrangement is considered to be a separate set.
For example:
For three singletons: {X},{Y}, & {Z} in a set S, the "ordered & permuted power set" would consist of the following subsets:
{Empty}
{X}; {Y}; {Z};
{X,Y}; {Y,X}; {X,Z}; {Z,X}; {Y,Z}; {Z,Y}
{X,Y,Z}; {X,Z,Y}; {Y,X,Z}; {Z,X,Y}; {Y,Z,X}; {Z,Y,X}
For example:
For three singletons: {X},{Y}, & {Z} in a set S, the "ordered & permuted power set" would consist of the following subsets:
{Empty}
{X}; {Y}; {Z};
{X,Y}; {Y,X}; {X,Z}; {Z,X}; {Y,Z}; {Z,Y}
{X,Y,Z}; {X,Z,Y}; {Y,X,Z}; {Z,X,Y}; {Y,Z,X}; {Z,Y,X}