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In mathematics applied to computer science, Monge arrays, or Monge matrices, are mathematical objects named for their discoverer, the French mathematician Gaspard Monge.
An m-by-n matrix is said to be a Monge array if, for all i , j , k , ℓ {\displaystyle \scriptstyle i,\,j,\,k,\,\ell } such that
one obtains
So for any two rows and two columns of a Monge array the four elements at the intersection points have the property that the sum of the upper-left and lower right elements is less than or equal to the sum of the lower-left and upper-right elements.
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