From what I have learned in Introduction to Automata Theory, Languages, and Computation, regular expressions can be represented with $R^{(k)}_{ij}$.
I understand that $i$ and $j$ represent the starting state and the closing state respectively. However, I am still trying to understand the purpose of $k$.
To put it simply, what does $k$ stand for in $R^{(k)}_{ij}$?
Side note: Link to the book is here.