Tilted Corners in Integer Grids
Abstract
It was proved by Ron Graham and the second author that for any coloring of the N × N grid using fewer than N colours, one can always find a monochromatic isosceles right triangle, a triangle with vertex coordinates (x, y),(x + d, y), and (x, y + d). In this paper we are asking questions where not only axis-parallel, but tilted isosceles right triangles are considered as well. Both colouring and density variants of the problem will be discussed.
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