let g be the set of all permutations of the set 1 2 n and let n be an integer 2 for each g let x

Name: let g be the set of all permutations of the set 1 2 n and let n be an integer 2 for each g let x be the number of inversions for ie the number of pairs i j with 1 i j n such that i j calcula 54624
Uploaded: 2023-08-11T04:57:11-08:00
Duration: 4 min 12 s
Channel: Madhur L
Description: let g be the set of all permutations of the set 1 2 n and let n be an integer 2 for each g let x be the number of inversions for ie the number of pairs i j with 1 i j n such that i j calcula 54624

Question

Suman K · Accepted Answer

First, we need to find the total number of possible permutations of the set {1, 2, ..., n}. This

Question

Let G be the set of all permutations of the set { 1, 2, . . . , n }, and let n be an integer ≥ 2. For each σ ∈ G, let X(σ) be the number of inversions for σ, i.e., the number of pairs (i, j) with 1 ≤ i < j ≤ n such that σ(i) > σ(j). Calculate the average value of X:

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