  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 $2n$
