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 log log N colors, 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 coloring and density variants of the problem will be discussed.

Locations

• arXiv (Cornell University) - View - PDF
• Zenodo (CERN European Organization for Nuclear Research) - View - PDF
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