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On Rado conditions for nonlinear Diophantine equations
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Barrett, Jordan Mitchell, Lupini, Martino and Moreira, Joel (2021) On Rado conditions for nonlinear Diophantine equations. European Journal of Combinatorics, 94 . 103277. doi:10.1016/j.ejc.2020.103277
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Official URL: https://doi.org/10.1016/j.ejc.2020.103277
Abstract
Building on previous work of Di Nasso and Luperi Baglini, we provide general necessary conditions for a Diophantine equation to be partition regular. These conditions are inspired by Rado’s characterization of partition regular linear homogeneous equations. We conjecture that these conditions are also sufficient for partition regularity, at least for equations whose corresponding monovariate polynomial is linear. This would provide a natural generalization of Rado’s theorem.
We verify that such a conjecture holds for the equations and for such that or . To deal with these equations, we establish new results concerning the partition regularity of polynomial configurations in such as , building on the recent result on the partition regularity of .
| Item Type: | Journal Article | ||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Diophantine equations , Polynomials | ||||||||||||||||||
| Journal or Publication Title: | European Journal of Combinatorics | ||||||||||||||||||
| Publisher: | Academic Press | ||||||||||||||||||
| ISSN: | 0195-6698 | ||||||||||||||||||
| Official Date: | May 2021 | ||||||||||||||||||
| Dates: |
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| Volume: | 94 | ||||||||||||||||||
| Article Number: | 103277 | ||||||||||||||||||
| DOI: | 10.1016/j.ejc.2020.103277 | ||||||||||||||||||
| Status: | Peer Reviewed | ||||||||||||||||||
| Publication Status: | Published | ||||||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||||||||
| RIOXX Funder/Project Grant: |
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