I'm reading Lothaire: Combinatorics on words the infinite series part and I have a small problem: I do not understand what is on the page 12 $(\sigma^i)_{i\geq 0}$ and why is $\langle \sigma^i,w\rangle =0$ for $i\geq |w|+1$ ?
In the text they define $\sigma_i$ but not $\sigma^i$. One can think that $\sigma^i$ is just the $i-$th power monomial, but still I do not follow the above implication that $\langle \sigma^i,w\rangle =0$ for $i\geq |w|+1$.
