Answered: 6. Show that a cycle of odd length is… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 51E

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6. 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) ( 193 ) ( 26 ) ( 4 5 10 ) (78)
(ii) ( 19326 ) ( 4
5 10 78),
(iii) ( 1932645 10).

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6. 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) (19 3) (2 6) (4 5 10 ) (78) 1 9 3 2 6) (4 5 10 7 8), (iii) 1 9 3 2 6 4 5 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 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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