For the discrete memoryless sources with a countably infinite alphabet, we prove that for any positive integer $k$, there exists a corresponding probability interval such that if the largest symbol probability $p_{1}$ falls in this interval, the optimal code length for the symbol equals $k$. Furthermore, for infinite sources, we provide a criterion to determine probability distributions whose optimal code length assignment follows the pattern $l^{best}_{i}=i$, for $i\ge 1$. Compared with the existing conclusion for anti-uniform sources, the proposed criterion requires less information for verification.

翻译：对于具有可数无限字母表的离散无记忆信源，我们证明：对任意正整数$k$，存在一个对应的概率区间，使得当最大符号概率$p_{1}$落在此区间内时，该符号的最优码长等于$k$。此外，针对无限信源，我们提出一个判据，用以确定其最优码长分配符合模式$l^{best}_{i}=i$（$i\ge 1$）的概率分布。与现有针对反均匀信源的结论相比，该判据所需的验证信息更少。