**Monge Array**

In 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 such that

one obtains

So whenever we pick two rows and two columns of a Monge array (a 2 × 2 sub-matrix) and consider the four elements at the intersection points, the sum of the upper-left and lower right elements (across the main diagonal) is less than or equal to the sum of the lower-left and upper-right elements (across the antidiagonal).

This matrix is a Monge array:

For example, take the intersection of rows 2 and 4 with columns 1 and 5. The four elements are:

- 17 + 7 = 24
- 23 + 11 = 34

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.

Read more about Monge Array: Properties, Applications

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