de Bruijn序列的差异性研究
Investigating the discrepancy property of de Bruijn sequences
摘要：
二进制字符串的差异是指给定二进制字符串的所有可能子串上1的数量和0的数量之间的最大（绝对）差异。我们提供了一个调查的差异，已知的简单结构的de Bruijn序列。此外，我们证明了结构，达到$Θ(n)$的下限和一个新的建设，达到以前已知的上限$Θ(\frac{2^n}{\sqrt{n}})$。这扩展了Cooper和Heitsch的工作~[ \emph{Discrete Mathematics}，310（2010）]。
英文摘要：
The discrepancy of a binary string refers to the maximum (absolute) difference between the number of ones and the number of zeroes over all possible substrings of the given binary string. We provide an investigation of the discrepancy of known simple constructions of de Bruijn sequences. Furthermore, we demonstrate constructions that attain the lower bound of $Θ(n)$ and a new construction that attains the previously known upper bound of $Θ(\frac{2^n}{\sqrt{n}})$. This extends the work of Cooper and Heitsch~[\emph{Discrete Mathematics}, 310 (2010)].
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