Ramsey properties of nonlinear Diophantine equations

@article{Nasso2016RamseyPO,
  title={Ramsey properties of nonlinear Diophantine equations},
  author={Mauro Di Nasso and Lorenzo Luperi Baglini},
  journal={arXiv: Combinatorics},
  year={2016}
}
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23 Citations
Highly Influential Citations
2
Background Citations
11
Methods Citations
9
Results Citations
1

23 Citations

Partition Regularity of Equations
Diophantine equations have been studied throughout the history of mathematics. Initially considered by Diophantus of Alexandria, a Hellenistic mathematician from the third century CE, they include…
Ultrafilters, monads and combinatorial properties
We use nonstandard methods, based on iterated hyperextensions, to develop applications to Ramsey theory of the theory of monads of ultrafilters. This is performed by studying in detail arbitrary…
ec 2 01 7 Ultrafilters , monads and combinatorial properties
We use nonstandard methods, based on iterated hyperextensions, to develop applications to Ramsey theory of the theory of monads of ultrafilters. This is performed by studying in detail arbitrary…
Nonstandard characterisations of tensor products and monads in the theory of ultrafilters
TLDR
Nonstandard methods, based on iterated hyperextensions, are used to develop applications to Ramsey theory of the theory of monads of ultrafilters, which extends to arbitrary sets and properties methods previously used to study partition regular Diophantine equations on N.
Nonstandard characterisations of tensor products and monads in the theory of ultrafilters
We use nonstandard methods, based on iterated hyperextensions, to develop applications to Ramsey theory of the theory of monads of ultrafilters. This is performed by studying in detail arbitrary…
Nonstandard characterizations of tensor products and monads in the theory of ultra lters
We use nonstandard methods, based on iterated hyperextensions, to develop applications to Ramsey theory of the theory of monads of ultralters. This is performed by studying in detail arbitrary tensor…
On Rado conditions for nonlinear Diophantine equations
Partition regularity of affine algebraic plane curves
We characterise all systems of Diophantine equations in two variables admitting infinitely many monochromatic solutions in N . Extending Rado’s Theorem, we prove that a system of polynomial equations…
Rado equations solved by linear combinations of idempotent ultrafilters
Rado's criterion over squares and higher powers
We establish partition regularity of the generalised Pythagorean equation in five or more variables. Furthermore, we show how Rado's characterisation of a partition regular equation remains valid…
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References

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Image Partition Regularity of Matrices
Many of the classical results of Ramsey Theory, including those of Hilbert, Schur, and van der Waerden, are naturally stated as instances of the following problem: given a u × ν matrix A with…
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