From Permutations to Horizontal Visibility Patterns of Periodic Series

Periodic series of period T can be mapped into the set permutations [T−1]={1,2,3,…,T−1}. These classified according to relative ordering their elements by horizontal visibility map. We prove that number classes for each coincides with triangulations polygon T+1 vertices that, as is well known, Catalan CT−1. also study robustness against Gaussian noise permutation patterns and show there are periodic better resist increase variance noise.