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Exercise 14.4.25. In light of what you discovered in the previous exercise, write each cycle as a product of transpositions:

Exercise 14.4.25. In light of what you discovered in the previous exercise, write each cycle as a product of transpositions:

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 14.4.25 part E and F. Please show step by step and explain

14.4.3 Transpositions and inverses The simplest nontrivial cycles are those of length 2. We will show that these 2-cycles are convenient “building blocks" which can be used to construct all other cycles. Definition 14.4.23. Cycles of length 2 are called transpositions. We will often denote transpositions by the symbol 7 (the greek letter “tau"). Exercise 14.4.24. Compute the following products: (a) (14)(13)(12) (d) (49)(48)(47)(46)(45) (b) (14)(18)(19) (c) (16)(15)(14)(13)(12) (e) (12)(13)(14)(15)(16)(17)(18) Exercise 14.4.25. In light of what you discovered in the previous exercise, write each cycle as a product of transpositions: (a) (1492) (c) (472563) (e) (a1a2aza5a6) (b) (12345) (d) (a1a2a3) (f) (a1a2a3a5agazas)
Transcribed Image Text:14.4.3 Transpositions and inverses The simplest nontrivial cycles are those of length 2. We will show that these 2-cycles are convenient “building blocks" which can be used to construct all other cycles. Definition 14.4.23. Cycles of length 2 are called transpositions. We will often denote transpositions by the symbol 7 (the greek letter “tau"). Exercise 14.4.24. Compute the following products: (a) (14)(13)(12) (d) (49)(48)(47)(46)(45) (b) (14)(18)(19) (c) (16)(15)(14)(13)(12) (e) (12)(13)(14)(15)(16)(17)(18) Exercise 14.4.25. In light of what you discovered in the previous exercise, write each cycle as a product of transpositions: (a) (1492) (c) (472563) (e) (a1a2aza5a6) (b) (12345) (d) (a1a2a3) (f) (a1a2a3a5agazas)
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