Levels of Permutation Sets

Corresponding to each line of any permutation set, there is considered the largest integer so far when doing a left to right scan. As a consequence, there is generated a set of step functions. To define proper subsets of the set of step functions, Foley uses concepts he defines as takeover, level, jump from, quiescence, jump to, and route. Through functions and algorithms, Foley is able to compute the expectations and expected values corresponding to the concepts.

Special lines and special points are also computed. This comprehensive and straightforward recreation of the mathematical steps taken will allow any student of higher level mathematics to understand the concepts used by Foley.