Divisor methods are well known to satisfy house monotonicity, which allows representative seats to be allocated sequentially. We focus on stationary divisor methods defined by a rounding cutpoint $c \in [0,1]$. For such methods with integer-valued votes, the resulting apportionment sequences are periodic. Restricting attention to two-party allocations, we characterize the set of possible sequences and establish a connection between the lexicographical ordering of these sequences and the parameter $c$. We then show how sequences for all pairs of parties can be systematically extended to the $n$-party setting. Further, we determine the number of distinct sequences in the $n$-party problem for all $c$. Our approach offers a refined perspective on size bias: rather than viewing large parties as simply receiving more seats, we show that they instead obtain their seats earlier in the apportionment sequence. Of particular interest is a new relationship we uncover between the sequences generated by the smallest divisor (Adams) and greatest divisor (D'Hondt or Jefferson) methods.

翻译：除数法因满足席位单调性而广为人知，这使得代表席位可以按顺序分配。我们关注由舍入临界点$c \in [0,1]$定义的固定除数法。对于此类处理整数值选票的方法，所产生的分配序列具有周期性。聚焦于两党分配的情形，我们刻画了可能序列的集合，并建立了这些序列的字典序与参数$c$之间的关联。随后，我们展示了如何将针对所有政党对的序列系统地推广至$n$党场景。此外，我们确定了$n$党问题中对于所有$c$值不同序列的数量。我们的方法为规模偏见提供了更精细的视角：与其简单地将大党视为获得更多席位，我们证明它们实际上是在分配序列中更早地获得席位。特别值得关注的是，我们揭示了最小除数法（亚当斯法）与最大除数法（顿特法或杰斐逊法）所生成序列之间的一种新关系。