A sequence may be decomposed into a *dictionary*, $\Delta$, and a *pattern*, $(\Psi_i)$, where the dictionary specifies which letters from the alphabet have appeared and the pattern specifies the order in which these letters have appeared [@OrlitskySZ2004]. For a sequence $(x_i)$, dictionary entry $\delta_k \in \mathcal{X}$ is the $k$th distinct letter in the sequence and pattern entry $\psi_i \in \mathbb{Z}^{+}$ is the dictionary index of the $i$th letter in the sequence. Note that the type of a pattern, denoted as $\{\Psi_i\}$, and the pattern of a multiset, denoted as $\Psi(\{X_i\})$, are the same. It can be seen that a multiset is determined by $\Delta$ and $\{\Psi_i\}$; the order of the pattern, $J(\Psi)$, is not needed.

Based on [@OrlitskySVZ2006], we show that the entropy rate of a multiset generated by a discrete finite-entropy stationary process and the entropy rate of its pattern are equal. First note that the dictionary of a sequence and the dictionary of its associated multiset are the same; we use $\Delta$ to signify either one. Since $\{X_i\}$ determines $\Psi(\{X_i\})$ and since given $\{\Psi_i\}$, there is a one-to-one correspondence between $\{X_i\}$ and $\Delta$, $$H(\{X_i\}) = H(\{\Psi_i\}) + H(\{X_i\} \mid \{\Psi_i\}) = H(\{\Psi_i\}) + H(\Delta \mid \{\Psi_i\}) \mbox{.}$$ If 