This paper mentions that any ordinal $\alpha < \epsilon_0$ can be written uniquely as $\alpha = \omega^\beta(\gamma+1)$, where $\beta<\alpha$.
Does this presentation have a name? Also, how would one get $\omega^\beta(\gamma+1)$ for a given $\alpha$? I played with this for a while and got stuck when setting $\alpha$ to, say, $\omega^\omega+1$. (Or is this just Cantor normal form disguised?)