Some Aspects of the Random Sequence

Abstract

This is primarily a review of combinatorial problems connected with ballot problems, runs, records, and amalgamation, but numerous new results and applications occur throughout the paper. The early history of the classical ballot problem is clarified, and many recent generalizations and applications are noted. For runs and records, the main emphasis is on the derivation of the null-hypothesis distributions, with only passing reference to asymptotics and non-null distributions. An appendix lists recent work on the Kolmogorov and Smirnov statistics. There are 183 references.