Partition regularity of the three-term reciprocal pattern
Partition regularity of the three-term reciprocal pattern
A finite coloring of is a coloring using finitely many colors. A pattern is partition regular over if every finite coloring of admits parameters making all entries of the pattern the same color.
Three-term reciprocal-pattern conjecture. The pattern
is partition regular over .
This is weaker than the reciprocal parallelogram conjecture, since it omits , but the paper states that even this weaker pattern is not known.
Sources & referencesView supporting material
Primary source
Ryan Alweiss, “Monochromatic Sums and Products over Q”, arXiv:2307.08901 (2026).
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