#Type/Definition #Topic/Linear_Algebra

Types: N/A
Examples: N/A
Constructions: 16.5 Permutation Definition of Determinant, 16.2.3 Sign of a Permutation
Generalizations: 16.2 Symmetric Groups

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Set of All Inversions for a Given π∈Sn

Let π∈Sn be given. Then, let the set of all inversions with respect to π be

Inv(π)={(i,j):i,j∈[n],i<j, and π(i)>π(j)}