Year: 2025
Type: article
Abstract: In this paper, we review certain combinatorial properties of some big sets, namely, sets with positive upper Banach density and piecewise syndeticity. In the process to do so, we give a proof of the upper density polynomial version of Furstenberg-Glasner's 定理, and using ergodic tools, we show that N_A(C) is piecewise syndetic in Z² if C=A-B, where A,B⊆ Z are two subsets of Z with positive upper Banach density. Moreover, we provide a simpler dynamical proof of Jin's 定理, i.e., the above mentioned C=A-B is piecewise syndetic, and give an affirmative answer to a question by Kra et al. when the set involved is piecewise syndetic.
Source: Scientia Sinica Mathematica
Authors: Ye Xiangdong, Huang Wen, Shao Song
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4408552919