While the linear partition regular polynomials have been characterized by Richard Rado in the 1930’s, very few results are known in the nonlinear case. Our aim is to prove that, on ℕ, there are at least two interesting classes of partition regular nonlinear polynomials. Our approach is based on the study of ultrafilters on ℕ from the point of view of Nonstandard Analysis. A particularity of this technique is that the proofs of the main results can be carried out by almost elementary algebraic considerations.
Partition regularity of nonlinear polynomials: a nonstandard approach / L.L. Baglini (CRM SERIES). - In: The Seventh European Conference on Combinatorics, Graph Theory and Applications : EuroComb 2013 / [a cura di] J. Nesetril, M. Pellegrini. - Prima edizione. - [s.l] : Springer, 2013. - ISBN 9788876424748. - pp. 407-412 [10.1007/978-88-7642-475-5_65]
Partition regularity of nonlinear polynomials: a nonstandard approach
L.L. Baglini
2013
Abstract
While the linear partition regular polynomials have been characterized by Richard Rado in the 1930’s, very few results are known in the nonlinear case. Our aim is to prove that, on ℕ, there are at least two interesting classes of partition regular nonlinear polynomials. Our approach is based on the study of ultrafilters on ℕ from the point of view of Nonstandard Analysis. A particularity of this technique is that the proofs of the main results can be carried out by almost elementary algebraic considerations.
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