Using the language of set algebra (such as cosets) and automata (for example, computation for a string manipulation), the authors consider the number of allowable orderings possible for a string that is processed through a limited buffered priority queue. In particular, they show that over all n strings of uniquely ordered characters, with a buffer size of 2, the number of possible output strings can be determined in O ( n² ). They also show that, if the string is binary-valued, one can use a formula found in de Bruijn et al. [1] to calculate the number of possible output sequences in O(size of buffer).