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.

About the Author

James M. Foley is a computer programmer for the Social Security Administration. Foley decided to write Levels of Permutation Sets while designing a memory simulator for a SNOBOL4 interpreter. A lifetime resident of Maryland, Foley earned his bachelors degree from Towson University in 1964. In addition to reading and writing, Foley also enjoys the opera and computers. Levels of Permutation Sets is his first published book.