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Show that a cycle of odd length is an even permutation, and a cycle of even length is an odd permutation. Hence determine which of the following members of S10 are even, or odd: (i) ( 1 9 3) (2 6 ) ( 4 (ii) (1 9 3 2 6) (4 (iii) ( 1 9326 4 5 5 10) (78) 5 10 7 8 ), 10).

Show that a cycle of odd length is an even permutation, and a cycle of even length is an odd permutation. Hence determine which of the following members of S10 are even, or odd: (i) ( 1 9 3) (2 6 ) ( 4 (ii) (1 9 3 2 6) (4 (iii) ( 1 9326 4 5 5 10) (78) 5 10 7 8 ), 10).

Advanced Engineering Mathematics
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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Show that a cycle of odd length is an even permutation, and a cycle of even length is an odd permutation. Hence determine which of the following members of S10 are even, or odd: (i) (1 9 3) (2 6) (4 5 10) (78) (ii) (1 9 3 2 6 ) (4 5 10 7 8), (iii) ( 1 9 3 2 6 4 5 10 ).
Transcribed Image Text:Show that a cycle of odd length is an even permutation, and a cycle of even length is an odd permutation. Hence determine which of the following members of S10 are even, or odd: (i) (1 9 3) (2 6) (4 5 10) (78) (ii) (1 9 3 2 6 ) (4 5 10 7 8), (iii) ( 1 9 3 2 6 4 5 10 ).
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