we can find the different cycle types of S3 and classified the 6 permutations of S3 accordingly. Write down all the cycle types for S4 and find the cycle type for each of the 24 permutations of S4 Resultn!Sn has'2*. na d,! dg! .. dn!permutations of kype [i^ gt. nte ]Example5!Ss has P'a!3! 1!5!2-s! [P2].= lo permutations of bypeTheyare(12) (3) (4) (5), (13) (2) (4)(8), (14) (2)()(),(15)(2)(3) (4), (23) (1) (4) (5), (24) (1) (a) (S),(25) (1)(3) (4),(34) (1) (2) (5), (35) (1) (2) (4),(45) (1)(2) (3),

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Answered: we can find the different cycle types…

we can find the different cycle types of S3 and classified the 6 permutations of S3 accordingly. Write down all the cycle types for S4 and find the cycle type for each of the 24 permutations of S4

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

we can find the different cycle types of S₃ and classified the 6 permutations of S₃ accordingly. Write down all the cycle types for S₄ and find the cycle type for each of the 24 permutations of S₄

Result
n!
Sn has
'2*. na d,! dg! .. dn!
permutations of kype [i^ gt. nte ]
Example
5!
Ss has P'a!3! 1!
5!
2-s! [P2].
= lo permutations of bype
They
are
(12) (3) (4) (5), (13) (2) (4)(8), (14) (2)()(),
(15)(2)(3) (4), (23) (1) (4) (5), (24) (1) (a) (S),
(25) (1)(3) (4),
(34) (1) (2) (5), (35) (1) (2) (4),
(45) (1)(2) (3),

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