# One-line notation for permutations

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## Definition

Consider a finite set and an ordering of the elements of , with the elements (in order), given as . For a permutation of , the one-line notation for is the string .

The one-line notation for a permutation is a compressed form for the two-line notation where the first line is omitted because it is implicitly understood.

For instance, for permutations on the set with the standard ordering, we can simply write the second line of the two-line notation where the first line is the standard ordering. For instance, consider a permutation with two-line notation:

Here, the first line is the standard ordering, and we can write the permutation using the one-line notation as: