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- W4288055403 abstract "We present a short ultrafilter proof of the existence of monochromatic exponential triples ${a, b, b^a}$ in any finite coloring of the natural numbers. The proof is given from scratch and uses only Ramsey's theorem, the notion of asymptotic density and the definition of ultrafilter as prerequisites. We then generalize the construction using a special ultrafilter whose existence is well known in the algebra of ultrafilters, and prove a new result on the existence of infinite monochromatic exponential patterns." @default.
- W4288055403 created "2022-07-28" @default.
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- W4288055403 date "2022-07-24" @default.
- W4288055403 modified "2023-09-29" @default.
- W4288055403 title "Monochromatic exponential triples: an ultrafilter proof" @default.
- W4288055403 doi "https://doi.org/10.48550/arxiv.2207.11764" @default.
- W4288055403 hasPublicationYear "2022" @default.
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