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Let be the permutation of the letters A through Z that

Chapter 5, Problem 21E

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QUESTION:

Problem 21E

Let σ be the permutation of the letters A through Z that takes each letter to the one directly below it in the display following. Write s in cycle form.

A B C D E F G H I J K L M NO P Q R S T U V W X Y Z

H D B G J E C M I L O N P F K R U S A W Q T V Z X Y

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QUESTION:

Problem 21E

Let σ be the permutation of the letters A through Z that takes each letter to the one directly below it in the display following. Write s in cycle form.

A B C D E F G H I J K L M NO P Q R S T U V W X Y Z

H D B G J E C M I L O N P F K R U S A W Q T V Z X Y

ANSWER:

Step 1 of 6

Consider the following permutation

Starting from the first element (A), the algorithm for solving problems like this as follows

1, Take an element from the original (unpermitted) set and call it x.

2. Note the mapping of the above element by. That is y such that

3. Look for an entry of the y in the original set. Note its mapping z, that is

4. Continue unit a mapped element which is x (the element first started out with) is obtained.

5. This comprises one cycle. Repeat 1-4 until an element is exhausted.

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