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4. Bijections and Permutations: a. Let t= 263198475 in one-line notation. Give two-line notation and cycle notation. Then its inverse, square in cycle notation. Show also tt = id.

4. Bijections and Permutations: a. Let t= 263198475 in one-line notation. Give two-line notation and cycle notation. Then its inverse, square in cycle notation. Show also tt = id.

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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### Bijections and Permutations: #### a. Let \(\tau = 263198475\) in one-line notation. Convert this into two-line notation and cycle notation. Then, find its inverse and the square in cycle notation. Also, demonstrate that \(\tau \cdot \tau^{-1} = \text{id}\). #### b. Describe the rotations of an equilateral triangle using permutations. (Hint: Use 120-degree rotations.) Identify the identity permutation and calculate the inverses of each rotation.
Transcribed Image Text:### Bijections and Permutations: #### a. Let \(\tau = 263198475\) in one-line notation. Convert this into two-line notation and cycle notation. Then, find its inverse and the square in cycle notation. Also, demonstrate that \(\tau \cdot \tau^{-1} = \text{id}\). #### b. Describe the rotations of an equilateral triangle using permutations. (Hint: Use 120-degree rotations.) Identify the identity permutation and calculate the inverses of each rotation.
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