All sums of h distinct terms of a sequence
All sums of h distinct terms of a sequence
复制标题
序列的 h 个不同项的所有和
DOI：
10.1016/j.ejc.2014.05.002
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发表时间：
2014
影响因子：
1
通讯作者：
Fang Jin-Hui
中科院分区：
文献类型：
--
作者：
Chen Yong-Gao;Fang Jin-Hui
对A⊆Z，我们研究了A的h个成对不同元素之和的序列中的空位.例如，证明了：对任意整数h≥3，存在A⊆Z，使得每个整数都可以唯一地(忽略顺序)表示为A的h的和，而不一定是A的不同元素.对于任意整数ℓ≥1，在A的所有ℓ成对不同元素的和序列中，空位可以任意大.本文提出了几个问题。
Abstract For A⊆ Z, we study the gaps in the sequence of all sums of h pairwise distinct elements of A. For example, the following result is proved: for any integer h≥ 3, there exists A⊆ Z such that every integer can be uniquely (neglecting the order) represented as a sum of h not necessarily distinct elements of A, and for any integer ℓ≥ 1, in the sequence of all sums of ℓ pairwise distinct elements of A, the gaps can be arbitrarily large. Several questions are posed in this paper.