PROBLEMS IN ADDITIVE NUMBER THEORY, IV: NETS IN GROUPS AND SHORTEST LENGTH g-ADIC REPRESENTATIONS
PROBLEMS IN ADDITIVE NUMBER THEORY, IV: NETS IN GROUPS AND SHORTEST LENGTH g-ADIC REPRESENTATIONS
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DOI：
10.1142/s1793042111004940
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发表时间：
2011-12
影响因子：
0.7
通讯作者：
M. Nathanson
中科院分区：
文献类型：
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作者：
M. Nathanson
在度量几何中的网的数论模拟提出了新的问题，并在组合和加法数论中产生了新的结果。例如，对于一个固定的整数g ≥ 2，研究关于生成集Ag = {0}<${± gi：i = 0，1，2，.}的整数加性群中的h-网需要关于Ag的整数的字长的知识。描述了整数的g-adic表示，其在算法上产生最短长度的表示。还讨论了加法补和加法渐近补，以及与之相关的极小性问题。
The number theoretic analog of a net in metric geometry suggests new problems and results in combinatorial and additive number theory. For example, for a fixed integer g ≥ 2, the study of h-nets in the additive group of integers with respect to the generating set Ag = {0} ∪ {± gi : i = 0, 1, 2, …} requires a knowledge of the word lengths of integers with respect to Ag. A g-adic representation of an integer is described that algorithmically produces a representation of shortest length. Additive complements and additive asymptotic complements are also discussed, together with their associated minimality problems.