What mathematical formulation that can help me to generate all possible (N x N) matrices where the sum of all elements inside each matrix equal constant number M ? Note that: M > N If it can be solved using combinations and permutations, how can I formulate it ?
2026-03-27 16:20:03.1774628403
combinations and permutations, how can I formulate it?
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If the positions of the matrix are distinct you are looking for weak compositions of $M$ into $N^2$ pieces. There are ${M+N^2-1 \choose N^2-1}$ of them. The Wikipedia article derives this.