Comparative analysis of the original and amplitude permutations

We compare the two basic ordinal patterns, i.e., the original and amplitude permutations, used to characterize vector structures. The original permutation consists of the indexes of reorganized values in the original vector. By contrast, the amplitude permutation comprises the positions of values in the reordered vector, and it directly reflects the temporal structure. To accurately convey the structural characteristics of vectors, we modify indexes of equal values in permutations to be the same as, for example, the smallest or largest indexes in each group of equalities. Overall, we clarify the relationship between the original and amplitude permutations. And the results have implications for time- and amplitude-symmetric vectors and will lead to further theoretical and experimental studies.