Prove the Result Classificalion of permuta bionsConsider the disjoint agele decomposition of Te Sn. Suppose it hasa, l-gcles, ds 2-cycles, dy 3-cgcles , . , dn n-cycles.Then we say T has cycle type [1*z**gh. n].ExampleT - (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 elementspermutation swappinga 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 thuswrite T=(25).Resultn!2*..Sn haspermutations of kype [iizt. n]

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Answered: Result n! de!... dn! Sn has…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 16EQ

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only question 12 question about：THE S + N DECOMPOSITION
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In this problem we show how a general partial fraction expansion can be used to calculate many inverse Laplace transforms. Suppose that F(s)=P(s)Q(s),F(s)=P(s)Q(s), where Q(s) is a polynomial of degree n with n distinct zeros r1, …, rn, and P(s) is a polynomial of degree less than n. In this case it is possible to show that P(s)/Q(s) has a partial fraction expansion of the form (36) P(s)Q(s)=A1s−r1+⋯+Ans−rn,P(s)Q(s)=A1s−r1+⋯+Ans−rn, where the coefficients A1, …, An must be determined. Show that L−1{F(s)}=n∑k=1P(rk)Q′(rk)erkt.

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