10 citations · 17 across the 17 of their papers we have counts for
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A Van der Waerden-free proof of Rado's theorem
Mauro Di Nasso, Lorenzo Luperi Baglini
We present a proof of the sufficiency of Rado's condition for the partition regularity of linear Diophantine equations that avoids any use of van der Waerden's theorem. The proof i…
Asymptotic Ramsey theory of Diophantine equations
Lorenzo Luperi Baglini, Alessandro Vegnuti
We introduce the notion of asymptotic partition regularity for Diophantine equations. We show how this notion is at the core of almost all known negative results in the Ramsey theo…
Polynomial extension of the Stronger Central Sets Theorem
Sayan Goswami, Lorenzo Luperi Baglini, Sourav Kanti Patra
In [F81] Furstenberg introduced the notion of central set and established his famous Central Sets Theorem. Since then, several improved versions of Furstenberg's result have been f…
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…
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…
Partition regularity of polynomial systems near zero
Lorenzo Luperi Baglini
Recently, S.~Kanti Patra and Md.~Moid Shaik proved the existence of monochromatic solutions to systems of polynomial equations near zero for particular dense subsemigroups of $…