Results 1 to 2 of 2

Math Help - Quick Combinatoric Question

  1. #1
    Newbie
    Joined
    Apr 2011
    Posts
    1

    Quick Combinatoric Question

    Hey I need to know if I'm doing this right. Here's the Q:

    How many subsets X of [n] of size k are there, such that when the elements
    of X are arranged in increasing order, the dierence between successive pairs of
    elements is at least c.

    I don't think the latex compiler is working....
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,554
    Thanks
    785
    Is [n] the set {1, ..., n}?

    To form each X = {a_1, ..., a_k}, one is required to pick a certain number of elements of [n]: first, a_1, ..., a_k themselves and, second, c - 1 elements a_i + 1, ..., a_i + c - 1 for each 1 <= i < k. The remaining elements of [n] have to be spread between k + 1 intervals: from 1 to a_1, from a_k to n, and from a_i and a_{i+1}, 1 <= i < k. Ways to spread the remaining elements are in 1-1 correspondence with elements of X. You can use Stars and bars theorem.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Even vs. Odd in a combinatoric proof
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: January 2nd 2011, 01:48 AM
  2. Two combinatoric problems
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: August 21st 2010, 05:16 PM
  3. Need help with Combinatoric Proof
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 27th 2010, 09:21 PM
  4. Combinatoric sequence, please help me
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: September 5th 2007, 08:05 AM
  5. combinatoric identity
    Posted in the Statistics Forum
    Replies: 1
    Last Post: February 17th 2007, 05:24 PM

Search Tags


/mathhelpforum @mathhelpforum