Perfect matrix

Updated on Oct 28, 2023

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In mathematics, a perfect matrix is an m-by-n binary matrix that has no possible k-by-k submatrix K that satisfies the following conditions:

k > 3

the row and column sums of K are each equal to b, where b ≥ 2

there exists no row of the (m − k)-by-k submatrix formed by the rows not included in K with a row sum greater than b.

The following is an example of a K submatrix where k = 5 and b = 2:

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