We study Rado functionals and the maximal condition (first introduced in [2]) in terms of the partition regularity of mixed systems of linear equations and inequalities. By strengthening the maximal Rado condition, we provide a sufficient condition for the partition regularity of polynomial equations over some infinite subsets of a given commutative ring. By applying these results, we derive an extension of a previous result obtained in [8] concerning partition regular inhomogeneous polynomials in three variables and also conditions for the partition regularity of equations of the form H(xzρ, y) = 0, where ρ is a non-zero rational and H ∈ Z[x, y] is a homogeneous polynomial.

Rado functionals and applications / P. Arruda, L. Luperi Baglini. - (2022 Sep 16).

Rado functionals and applications

L. Luperi Baglini
2022

Abstract

We study Rado functionals and the maximal condition (first introduced in [2]) in terms of the partition regularity of mixed systems of linear equations and inequalities. By strengthening the maximal Rado condition, we provide a sufficient condition for the partition regularity of polynomial equations over some infinite subsets of a given commutative ring. By applying these results, we derive an extension of a previous result obtained in [8] concerning partition regular inhomogeneous polynomials in three variables and also conditions for the partition regularity of equations of the form H(xzρ, y) = 0, where ρ is a non-zero rational and H ∈ Z[x, y] is a homogeneous polynomial.
Settore MAT/01 - Logica Matematica
https://arxiv.org/abs/2209.07844
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/938915
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