Consider the following 3 permutations in S10: 0 = 1 2 3 4 5 6 7 8 1 4 5 6 8 10 7 9 2 9 10 3 fl= T= 1 2 2 5 10 4 9 3 4 5 6 7 7 6 1 2 3 4 5 6 7 8 9 10 10 9 8 4 3 2 1 5 6 7 8 3 9 10 8 1 (8.1) Compute 7μ-¹o. (8.2) Express as a product of disjoint cycles and then as a product of transpositions. (8.3) Find the smallest value of n so that " = i, where i is the identity permutation.
Consider the following 3 permutations in S10: 0 = 1 2 3 4 5 6 7 8 1 4 5 6 8 10 7 9 2 9 10 3 fl= T= 1 2 2 5 10 4 9 3 4 5 6 7 7 6 1 2 3 4 5 6 7 8 9 10 10 9 8 4 3 2 1 5 6 7 8 3 9 10 8 1 (8.1) Compute 7μ-¹o. (8.2) Express as a product of disjoint cycles and then as a product of transpositions. (8.3) Find the smallest value of n so that " = i, where i is the identity permutation.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
please do 8.3
Transcribed Image Text:QUESTION 8
Consider the following 3 permutations in S10:
0 =
1 2 3 4 5 6
7 8 9 10
1 4 5 6 8 10 7 9 2 3
= (₁
H=
1
T=
1 2 3 4 5 6 7
2 5 10 4 9 7 6
2 3 4 5 6
7 8 9 10
10 9 8 4 3 2 1 5 6 7
8 9 10
3 8 1
(8.1) Compute 7μ¹σ.
(8.2) Express μ as a product of disjoint cycles and then as a product of transpositions.
(8.3) Find the smallest value of n so that μ = i, where i is the identity permutation.
(8.4) Find ¹00
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