Tiling with Monotone Polyominos

A monotone polyomino is a set of grid cells pierced by a continuous monotone function f:[a,b]-> R. We prove that the minimum number of monotone polyominos in a tiling of the nxn lattice square is n. Surprisingly, this turns out to be equivalent with the statement that every triangulation of the nxn lattice square into minimum lattice triangles contains at least 2n right angled triangles.

Automated summary

The passage discusses the problem of monotone polyominoes and triangulations of lattice squares. It proves that the minimum number of monotone polyominoes in a tiling of the nxn lattice square is n, which is equivalent to the statement that every triangulation of the nxn lattice square into minimum lattice triangles contains at least 2n right angled triangles.