Long minimal zero-sum sequences over a finite subset of Z
Long minimal zero-sum sequences over a finite subset of Z
复制标题
Z 的有限子集上的长最小零和序列
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
曾详能
中科院分区：
文献类型：
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作者：
邓贵新;曾详能
设G是阿贝尔群，X是G的子集，S是X上的极小零和序列。称S在X中不可裂，如果S中不存在元素g，X中不存在两个元素x，y，使得g = x + y，并且新序列Sg−1xy仍然是极小零和序列。本文主要研究G = Z，X = [[−m，n]]，m，n ∈ N的情形. length.atn ≥ m2/2 − 1和m ≥ 6的条件下，得到了最小n +<$m/2 <$+ 2的不可分裂极小零和序列的结构.作为推论，达文波特常数D（[−m，n]]）在n ≥ m2/2−1时确定。本文还讨论了一般集合X <$Z的达文波特常数D（X）。
Let G be an abelian group (written additively), X be a subset of G and S be a minimal zero-sum sequence over X. S is called unsplittable in X if there do not exist an element g in S and two elements x, y in X such that g = x + y and the new sequence Sg−1xy is still a minimal zero-sum sequence. In this paper, we mainly investigate the case when G = Z and X = [[−m, n]] with m, n ∈ N. We obtain the structure of unsplittable minimal zero-sum sequences of length.at least n + ⌊m/2⌋ + 2 provided that n ≥ m2/2 − 1 and m ≥ 6. As a corollary, the Davenport constant D([[−m, n]]) is determined.when n ≥ m2/2−1. The Davenport constant D(X) for a general set X ⊂ Z is also discussed.