Results 1 to 5 of 5

Math Help - Integer Arrangement

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    12

    Integer Arrangement

    We want to arrange the integers 1,2,...,n (in a row) such that successive integers cannot be in adjacent positions. In how many ways can we do this for a general n?

    Okay, let a_n denote the number of such arrangements. Then we have
    a_2 = a_3 = a_4 = 0, a_5 = 2 (13524,14253). The only useful thing i could notice is that in forming the 5-integers arrangement, we can fix 1 and then add 3524 to 1 forwards and backwards. I think we can use this trick in any integer arrangement greater than 5. But how can we calculate the number of arrangements for larger numbers?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1783
    Awards
    1
    OK. Take you example of n=5.
    We cannot have 13425
    . But can we have 14325?
    Do you see my question? In 14325 the 43 are consecutive.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2008
    Posts
    12
    Yes,i see what you mean but still i can't use it for determining the number of arrangements for larger integers. Can you explain it a little more for a specific case?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1783
    Awards
    1
    Please answer the question.
    We cannot have 13425! We know that!
    But can we have 14325?
    Please answer.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Mar 2008
    Posts
    12
    No,we can't have 14325.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. help me on the arrangement please
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: December 31st 2010, 12:24 PM
  2. Replies: 12
    Last Post: December 18th 2010, 04:22 AM
  3. Replies: 13
    Last Post: August 3rd 2010, 04:16 AM
  4. Integer roots of integer polynomials
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: December 3rd 2009, 01:39 PM
  5. Raise integer to positive integer power
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 21st 2009, 01:20 PM

Search Tags


/mathhelpforum @mathhelpforum