和集的多项式大性与全遍历集
Polynomial largeness of sumsets and totally ergodic sets
摘要：
我们证明了（\N）的TE子集（这些集合可以被看作是“非周期”集合）的具有正上密度集的和集与任何具有整数系数的多项式的值集相交。即，对于任何（A \subset \N）TE集，对于任何（p（n）\in \Z [n]：0 {p（n）} > 0，p（n）\to_{n \to \infty} \infty）和正上密度的任何子集（B \subset \N），我们有（R_p = A+B \cap p（n）|n \in \N \} \neq \emptyset）。对于（A）一个WM集（TE集的子类），我们证明了（R_p）具有较低的密度1.此外，我们得到了后者的结果的情况下，几个多项式和几个WM集的推广。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
