I am reading Zeilberger's paper on repeated coin tossing (winning or losing a dollar each time), and I came upon the following:
If you factor a break-even sequence (i.e. with sum $0$) according to its sign-changes, and look at it as a sequence of $P$'s and $N$'s, we have the following regular expression $$ empty \vee P(NP)^{*} \vee P(NP)^{*}N \vee N(PN)^{*} \vee N(PN)^{*}P \quad, $$
where we call
a segment between two consecutive break-even times, where it was not losing in-between, a $P$-segment
and
a segment between two consecutive break-even times, where it was it not winning in-between, an $N$-segment.
I think Zeilberger is saying that any sequence of wins and losses is either empty, or a concatenation of a $P$-segment with an $(NP)^*$ segment, and so on. My question is, what does $*$ mean? I'm guessing it means repetition: $(X)^*=\emptyset\vee X \vee XX \vee XXX \vee \cdots$. Is this the right interpretation?