Math 360, Fall 2018, Assignment 11

I have found a very great number of exceedingly beautiful theorems."

- Pierre de Fermat

Carefully define the following terms, then give one example and one non-example of each:

1. Transposition (also known as a swap).
2. Even (permutation).
3. Odd (permutation).
4. Orbit (of a permutation).

Carefully state the following theorems (you do not need to prove them):

1. Theorem concerning permutations which are simultaneously even and odd.

Solve the following problems:

1. Section 9, problem 24.

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