#Type/Definition #Topic/Linear_Algebra

Types: N/A
Examples: 16.2 Symmetric Groups
Constructions: 16.1.1 Permutation of a Set A
Generalizations: N/A

Properties: 16.2.3 Sign of a Permutation
Sufficiencies: N/A
Questions: N/A

Permutation

Every permutation is a bijection, meaning it is:

  1. Onto: Rng(π)=[n]=codomain.
  2. One-to-one: If π(i)=k and π(j)=k, then i=j.

We will say

Snsymmetric group on n element={π:where π is a permutation on [n]}=set of all permutations of {n}