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How do I enumerate a family of 0-1 matrices

Asked by Paul Fishback on 25 Aug 2016
I'm trying to generate the family of all 10-by-3 matrices, where each matrix in the family, call it S, has the property that S(i,j)= 0 or 1 for i=1..10 and j=1..3, and that each of the 10 row sums of S equals 1, i.e. S(i,1)+S(i,2)+S(i,3)=1, for i=1..10.

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