1-Colored Archetypal Permutations and Strings of Degree n

New notions related to permutations are introduced here. We present the string of a 1-colored permutation as a closed planar curve, the fundamental 1-colored permutation as an equivalence class related to the equivalence in strings of the 1-colored permutations. We give formulas for the number of the 1-colored archetypal permutations of degree n. We establish an algorithm to identify the 1- colored archetypal permutations of degree n and we present the atlas of the 1-colored archetypal strings of degree n, n ≤ 7, based on this algorithm.