关于串串的最大指数和
On the maximal sum of exponents of runs in a string
摘要：
游程是重复$v$的字符串（作为子区间）中的包含最大出现次数，其周期为$p$，使得$2p \le |v|$。运行的指数定义为$|v|/p$，为$\ge 2$。我们展示了新的界限上的最大和的指数运行在一个字符串的长度$n$。我们的$4.1n$的上界优于Crochemore & Ilie（2008）的$5.6n$的已知最佳上界。使用二进制字族得到的$2.035n$的下界与Kolpakov和Kucherov（1999）的猜想相矛盾，Kolpakov和Kucherov猜想长度为$n$的串中游程的指数的最大和小于$2n$
英文摘要：
A run is an inclusion maximal occurrence in a string (as a subinterval) of a repetition $v$ with a period $p$ such that $2p \le |v|$. The exponent of a run is defined as $|v|/p$ and is $\ge 2$. We show new bounds on the maximal sum of exponents of runs in a string of length $n$. Our upper bound of $4.1n$ is better than the best previously known proven bound of $5.6n$ by Crochemore & Ilie (2008). The lower bound of $2.035n$, obtained using a family of binary words, contradicts the conjecture of Kolpakov & Kucherov (1999) that the maximal sum of exponents of runs in a string of length $n$ is smaller than $2n$
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