In this paper, we present an algorithm that enumerates a certain class of signed permutations, referred to as grid signed permutation classes. In the case of permutations, the corresponding grid classes are of interest because they are equivalent to the permutation classes that can be enumerated by polynomials. Furthermore, we apply our results to genome rearrangements and establish that the number of signed permutations with fixed prefix-reversal and reversal distance is given by polynomials that can be computed by our algorithm.

翻译：本文提出了一种枚举特定带符号置换类（称为网格带符号置换类）的算法。在置换情形下，相应的网格类具有研究价值，因其等价于可由多项式枚举的置换类。此外，我们将结果应用于基因组重排问题，并证明固定前缀反转距离和反转距离的带符号置换数量可由多项式给出，且这些多项式可通过本文算法计算。