论文标题
汇总的紧密结构定理
A tight structure theorem for sumsets
论文作者
论文摘要
令$ a = \ {0 = a_0 <a_1 <\ cdots <a _ {\ ell + 1} = b \} $是一组有限的非阴性整数。我们证明，前提是Shakan和第一作者最近猜想的$ n \ geqslant b- \ ell $，$ na $具有一定的易于描述的结构。我们还对无法改善此界限的那些集合$ a $进行了分类。
Let $A = \{0 = a_0 < a_1 < \cdots < a_{\ell + 1} = b\}$ be a finite set of non-negative integers. We prove that the sumset $NA$ has a certain easily-described structure, provided that $N \geqslant b-\ell$, as recently conjectured by Shakan and the first author. We also classify those sets $A$ for which this bound cannot be improved.
