群中的网、最小长度$g$ -进表示和最小加法补
Nets in groups, minimum length $g$-adic representations, and minimal additive complements
摘要：
度量几何中网的数论模拟提出了组合数论和加性数论中的新问题和新结果。例如，对于一个固定的整数g > 1，关于生成集A_g = {g^i：i= 0，1，2，.}需要关于A_g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。
英文摘要：
The number theoretic analogue of a net in metric geometry suggests new problems and results in combinatorial and additive number theory. For example, for a fixed integer g > 1, the study of h-nets in the additive group of integers with respect to the generating set A_g = {g^i:i=0,1,2,...} requires a knowledge of the word lengths of integers with respect to A_g. 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.
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。
