a combinatorial question

Discussion in 'Scientific Statistics Math' started by analyst41, Nov 19, 2011.

  1. analyst41

    analyst41 Guest

    You have n objects and m slots, n >m .

    A "presentation" is a set of m distinct objects out of the n placed in
    the m slots.

    It is required that object j be presented count(j) times for j =
    1,2,....n.

    Is there a simple method to determine of a set of count values is
    feasible and if so lay out a method to obtain a feasible set of
    presentations.

    Thanks.
     
    analyst41, Nov 19, 2011
    #1
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  2. If I understand the problem, you're asking about a matrix of 0's and
    1's with prescribed row and column sums. Namely, if k = [count(1) +...
    + count(n)]/m, you want a k-by-n matrix of 0's and 1's with all row
    sums equal to m, and the j-th column sum equal to count(j). If that's
    your problem, you should look up the Gale-Ryser theorem.
     
    Butch Malahide, Nov 19, 2011
    #2
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