3 papers
math.CO2022
Rado functionals and applications
Paulo Henrique Arruda, Lorenzo Luperi Baglini
We study Rado functionals and the maximal condition (first introduced by J. M. Barret et al.) in terms of the partition regularity of mixed systems of linear equations and inequali…
math.CO2022
A limiting result for the Ramsey theory of functional equations
Lorenzo Luperi Baglini, Paulo Henrique Arruda
We study systems of functional equations whose solutions can be parameterized in function of one variable; our main result proves that the partition regularity (PR) of such systems…
math.CO2020
Rado equations solved by linear combinations of idempotent ultrafilters
Lorenzo Luperi Baglini, Paulo Henrique Arruda
We fully characterise the solvability of Rado equations inside linear combinations $a_{1}\U\oplus\dots\oplus a_{n}\U$ of idempotent ultrafilters $\U\inβ\Z$ by exploiting known rela…