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Permutations and directions of Integers

  1. Feb 22, 2009 #1
    Given this permutations {1,2....,n}, prove that the directions of 1 and 2 never change.

    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.
     
  2. jcsd
  3. Feb 22, 2009 #2

    Dick

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    I don't see any arrows here. I don't know what your problem or description means. Can you explain using a more standard mathematical notation?
     
  4. Feb 22, 2009 #3
    I don't know how to put arrows above the numbers.
     
  5. Feb 22, 2009 #4

    Dick

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    That's ok. I wouldn't understand what it meant anyway. What does the problem mean? How is {1,2,3,...,n} a permutation? Do you mean the cycle (1,2,3,...,n)? Your notation and adjectives like 'mobile' and 'direction' are pretty obscure for me.
     
  6. Feb 22, 2009 #5
    Basically you want to track how integers move in a permutation. I'm not sure how to explain it more than that. And I need to prove that 1 and 2 will always have a left facing direction.
     
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