Exploit additional diagonal and subdiagonal structure

Investigate whether properties of the diagonals below the main diagonal and of the subdiagonal of length n − 1 can be used to improve the upper bound R3(L) ≤ 493 for monochromatic Ls in 3-colored integer grids.

Background

The upper-bound arguments derive forced-color constraints from the main diagonal and its lower subdiagonals. The paper leaves unexamined whether further structural information from the diagonals below the main diagonal, together with the subdiagonal of length n − 1, can strengthen those arguments and reduce the current upper bound for R3(L).