# a combinatorial question

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

1. ### analyst41Guest

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

2. ### Butch MalahideGuest

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

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