Short k-radius sequences,k-difference sequences and universal cycles
Short k-radius sequences,k-difference sequences and universal cycles
复制标题
短k半径序列、k差序列和通用循环
DOI：
10.1002/jcd.21711
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发表时间：
2020
影响因子：
0.7
通讯作者：
e
中科院分区：
文献类型：
--
作者：
Zhang Xi;e
一个ary-radius序列是一个有限的元素序列，取自一个大小的字母表，其中任何两个不同的元素出现在序列中的某个地方。构造短半径序列的研究是由大数据传输中出现的一些问题激发的。设为任意任意半径序列的最短长度。我们证明了邦迪等人的结论对，并确定了对新无穷多的精确值。此外，我们研究了我们称之为差异的新序列，因为它们与半径序列有关，并且似乎本身很有趣。最后，我们回答了一个问题的最佳长度的包装和覆盖类似物的泛圈提出的Dobbski等人。
An‐ary‐radius sequence is a finite sequence of elements taken from an alphabet of sizein which any two distinct elements occur within distanceof each other somewhere in the sequence. The study of constructing short‐radius sequences was motivated by some problems occurring in large data transfer. Letbe the shortest length of any‐ary‐radius sequence. We show that the conjectureby Bondy et al is true for, and determine the exact values offor new infinitely many. Further, we investigate new sequences which we call‐difference, as they are related to‐radius sequences and seem to be interesting in themselves. Finally, we answer a question about the optimal length of packing and covering analogs of universal cycles proposed by Dębski et al.