PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

A limiting result for the Ramsey theory of functional equations

Volume 264 / 2024

Paulo Henrique Arruda, Lorenzo Luperi Baglini Fundamenta Mathematicae 264 (2024), 55-68 MSC: Primary 05D10; Secondary 11B75, 11D72, 11D61, 54D80 DOI: 10.4064/fm230621-5-10 Published online: 22 January 2024


We study systems of functional equations whose solutions can be parameterized by one of the variables. Our main result proves that the partition regularity (PR) of such systems can be completely characterized by the existence of constant solutions. As applications of this result, we prove the following:

$\bullet$ A complete characterization of PR systems of Diophantine equations in two variables over $\mathbb N$. In particular, we prove that the only infinitely PR irreducible equation in two variables is $x=y$.

$\bullet$ PR of $S$-unit equations and the failure of Rado’s Theorem for finitely generated multiplicative subgroups of $\mathbb C$.

$\bullet$ A complete characterization of the PR of two classes of polynomial exponential equations.


  • Paulo Henrique ArrudaFakultät für Mathematik
    Universität Wien
    1090 Wien, Austria
  • Lorenzo Luperi BagliniDipartimento di Matematica
    Università di Milano
    20133 Milano, Italy

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image