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Exercise 14.4.28. Express the following permutations as products of trans- positions. (a) (14356) (d) (17254)(1423)(154632) (b) (156)(234) (e) (142637)(2359) (c) (1426)(142) (f) (13579)(2468)(19753)(2864)

Exercise 14.4.28. Express the following permutations as products of trans- positions. (a) (14356) (d) (17254)(1423)(154632) (b) (156)(234) (e) (142637)(2359) (c) (1426)(142) (f) (13579)(2468)(19753)(2864)

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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Please do Exercise 14.4.28 part D and F and please show step by step and explain

Recall that we also know that any permutation can be written as a product of disjoint cycles, which leads to: Proposition 14.4.27. Any permutation of a finite set containing at least two elements can be written as the product of transpositions. PROOF. First write the permutation as a product of cycles: then write each cycle as a product of transpositions. Exercise 14.4.28. Express the following permutations as products of trans- positions. (a) (14356) (d) (17254)(1423)(154632) (b) (156)(234) (e) (142637)(2359) (c) (1426)(142) (f) (13579)(2468)(19753)(2864) Even the identity permutation id can be expressed as the product of trans- positions:
Transcribed Image Text:Recall that we also know that any permutation can be written as a product of disjoint cycles, which leads to: Proposition 14.4.27. Any permutation of a finite set containing at least two elements can be written as the product of transpositions. PROOF. First write the permutation as a product of cycles: then write each cycle as a product of transpositions. Exercise 14.4.28. Express the following permutations as products of trans- positions. (a) (14356) (d) (17254)(1423)(154632) (b) (156)(234) (e) (142637)(2359) (c) (1426)(142) (f) (13579)(2468)(19753)(2864) Even the identity permutation id can be expressed as the product of trans- positions:
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