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arXiv 0710.3718math.COmath.NT
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有限循环群中的加权序列

Weighted Sequences in Finite Cyclic Groups

David J. Grynkiewicz, Jujuan Zhuang

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摘要：

设$p>7$是素数，设$G=\Z/p\Z$，设$S_1=\prod_{i=1}^p g_i$和$S_2=\prod_{i=1}^p h_i$是两个序列，其项来自$G$。假设来自$S_1$或$S_2$的项的最大重数至多为$\frac{2p+1}{5}$。然后，我们表明，对于每个$g\in G$，存在一个置换$σ$的$1,2,..., p$，使$g=\sum_{i=1}^{p}(g_i\cdot h_{σ(i)})$。这个问题与A. Bialostocki关于加权子序列和和Erdens-Ginzburg-Ziv定理。

英文摘要：

Let $p>7$ be a prime, let $G=\Z/p\Z$, and let $S_1=\prod_{i=1}^p g_i$ and $S_2=\prod_{i=1}^p h_i$ be two sequences with terms from $G$. Suppose that the maximum multiplicity of a term from either $S_1$ or $S_2$ is at most $\frac{2p+1}{5}$. Then we show that, for each $g\in G$, there exists a permutation $σ$ of $1,2,..., p$ such that $g=\sum_{i=1}^{p}(g_i\cdot h_{σ(i)})$. The question is related to a conjecture of A. Bialostocki concerning weighted subsequence sums and the Erdős-Ginzburg-Ziv Theorem.

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。

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