论文标题

有限整数集的总和ii

Sums of Finite Sets of Integers, II

论文作者

Nathanson, Melvyn B.

论文摘要

令$ \ mathcal {a} $为有限的整数集,让$ h \ Mathcal {a} $表示$ h $ -fold of $ \ mathcal {a} $。令$(h \ Mathcal {a})^{(t)} $为$ h \ Mathcal {a} $的子集,由所有具有至少$ t $表示的整数组成,作为$ \ nathcal {a} $的$ h $ elements的总和。对于所有$ h \ geq H_T $,完全确定了集合$(H \ Mathcal {a})^{(t)} $的结构。

Let $\mathcal{A}$ be a finite set of integers, and let $h\mathcal{A}$ denote the $h$-fold sumset of $\mathcal{A}$. Let $(h\mathcal{A})^{(t)}$ be subset of $h\mathcal{A}$ consisting of all integers that have at least $t$ representations as a sum of $h$ elements of $\mathcal{A}$. The structure of the set $(h\mathcal{A})^{(t)}$ is completely determined for all $h \geq h_t$.

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