Permutation Set Properties

Consider a set of k elements. Let the elements be the first k positive integers. Consider the permutation set that corresponds to the first k positive integers. Let each element's order equal that element's value. At every line of the permutation set there exists an element or there exist the elements of the greatest order so far while doing a left to right scan. As a consequence, there exist ten permutation set properties. Expectations and expected values corresponding to most of the prope...