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math.CO2024
Partition regularity of generalized Pythagorean pairs
Nikos Frantzikinakis, Oleksiy Klurman, Joel Moreira
We address partition regularity problems for homogeneous quadratic equations. A consequence of our main results is that, under natural conditions on the coefficients , for a…
math.CO2023★ 1 cited
Partition regularity of Pythagorean pairs
Nikos Frantzikinakis, Oleksiy Klurman, Joel Moreira
We address a core partition regularity problem in Ramsey theory by proving that every finite coloring of the positive integers contains monochromatic Pythagorean pairs, i.e., $x,y\…
math.CO2016
Monochromatic sums and products in
Joel Moreira
An old question in Ramsey theory asks whether any finite coloring of the natural numbers admits a monochromatic pair . We answer this question affirmatively in a strong…