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Result n! de!... dn! Sn has permutations of ky pe [1i2* nte]

Result n! de!... dn! Sn has permutations of ky pe [1i2* nte]

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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Prove the Result 

Classificalion of permuta bions Consider the disjoint agele decomposition of Te Sn. Suppose it has a, l-gcles, ds 2-cycles, dy 3-cgcles , . , dn n-cycles. Then we say T has cycle type [1*z**gh. n]. Example T - (135 7 9) (24 6) (8 lo) in Sio has bype %3D [° 2' 3' 4° s' c° 7° g° q° 1o°] which we uswally write [235). • o= (12)(34)( 79) (5) (6) (P) (10) in S. has bype [I'2] •a trunsposition in Sn is a two elements permutation swapping a and b. It has cyele type [I**2']. • T = (2 5) (1) (3)(4) (6)(7)(8)(9) (10) is a transposition in S,. We usually omił l-cycles in an expression like this and thus write T=(25). Result n! 2*.. Sn has permutations of kype [iizt. n]
Transcribed Image Text:Classificalion of permuta bions Consider the disjoint agele decomposition of Te Sn. Suppose it has a, l-gcles, ds 2-cycles, dy 3-cgcles , . , dn n-cycles. Then we say T has cycle type [1*z**gh. n]. Example T - (135 7 9) (24 6) (8 lo) in Sio has bype %3D [° 2' 3' 4° s' c° 7° g° q° 1o°] which we uswally write [235). • o= (12)(34)( 79) (5) (6) (P) (10) in S. has bype [I'2] •a trunsposition in Sn is a two elements permutation swapping a and b. It has cyele type [I**2']. • T = (2 5) (1) (3)(4) (6)(7)(8)(9) (10) is a transposition in S,. We usually omił l-cycles in an expression like this and thus write T=(25). Result n! 2*.. Sn has permutations of kype [iizt. n]
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