Given this permutations {1,2....,n}, prove that the directions of 1 and 2 never change.(adsbygoogle = window.adsbygoogle || []).push({});

Proof: When generating permutations, one starts with everything having a left facing arrow. In order to determine what is mobile, the arrow must be pointing towards a smaller integer. 1 points to nothing so it is no mobile. 2 is mobile, however once it moves to the left it is no longer mobile. The remainder of the integers in {1,2,...,n} are mobile. Therefore, 1 and 2 will always point to the left since all the other integers are larger than those two.

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# Permutations and directions of Integers

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