Exercise 10.1. Let a, 3, 7 € Sym(10) be given as follows: α = B = Y = 0 3 1 2 3 4 5 6 7 8 0641 2598 0 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 0 (0 1 2 3 4 5 6 7 8 9) 4 5 2 6 18 97 3 a) Compute the number of inversions of a, 3, 7. b) Compute the parity of a, 3, 7.

Exercise 10.1. Let a, 3, 7 € Sym(10) be given as follows: α = B = Y = 0 3 1 2 3 4 5 6 7 8 0641 2598 0 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1 0 (0 1 2 3 4 5 6 7 8 9) 4 5 2 6 18 97 3 a) Compute the number of inversions of a, 3, 7. b) Compute the parity of a, 3, 7.

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

This is group theory question, please explain it using simple words step by step, thanks :)

Exercise 10.1. Let a, 3, 7 € Sym(10) be given as follows:
α =
B =
Y =
0
3
1 2 3 4 5 6 7 8
0641
2598
0
1 2 3 4
5
6
7 8 9
9 8 7 6 5 4 3 2 1 0
(0 1 2 3 4 5 6 7 8 9)
4 5 2 6 18 97
3
a) Compute the number of inversions of a, 3, 7.
b) Compute the parity of a, 3, 7.

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Follow-up Question

I found that the definition of parity is -1^(k), k is the number of inversion. for gamma, there are 18 inversions which implies the even parity. However, the numbe of its transposition is 9, so u said the parity is odd. I dont know which one is true.

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