Set Permutations

A reordering of a set.

Definition

A permutation is a Bijection $\sigma :\{1,2,\dots ,n\}\to \{1,2,\dots ,n\}$. A permutation exists in the set $S_n$ of all permutations.

Intuition

A permutation acts on a Tuple $\{1,\dots ,n\}$ giving us a new tuple $s\{\sigma (1),\dots ,\sigma (n)\}$.

Concepts

• Permutation Notation
• Sign of Permutation
• Permutation Orbit
• Every Permutation Can be Written as a Product of Disjoint Cycles