Polynomial largeness of sumsets and totally ergodic sets
| dc.creator | Fish, A. | |
| dc.date | 2007-11-20 | |
| dc.date.accessioned | 2026-07-07T08:44:04Z | |
| dc.date.available | 2026-07-07T08:44:04Z | |
| dc.description | We prove that a sumset of a TE subset of (\N) (these sets can be viewed as "aperiodic" sets) with a set of positive upper density intersects a set of values of any polynomial with integer coefficients., i.e. for any (A \subset \N ) a TE set, for any (p(n) \in \Z[n]: °{p(n)} > 0, p(n) \to_{n \to \infty} \infty ) and any subset (B \subset \N ) of positive upper density we have (R_p = A+B \cap \{p(n) | n \in \N \} \neq \emptyset). For (A ) a WM set (subclass of TE sets) we prove that (R_p ) has lower density 1. In addition we obtain a generalization of the latter result to the case of several polynomials and several WM sets. | |
| dc.description | Preliminary version | |
| dc.identifier | https://arxiv.org/abs/0711.3201 | |
| dc.identifier | http://arxiv.org/abs/0711.3201 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142529 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Combinatorics | |
| dc.title | Polynomial largeness of sumsets and totally ergodic sets | |
| dc.type | text |