Structural equivalence of $s$-tuples in random discrete sequences

Recently there appeared a significant number of papers investigating structural properties of random discrete sequences. They provide a large group of results on structurally equivalent intervals in such sequences. The goal of the present paper is to give a survey of the problems and the known results in this interesting area of discrete probability theory.
This research was supported by the Russian Foundation for Basic Research, grant 02–01–00266, by the grant 1758.2003.1 of the State support of the leading scientific schools of the Russian Federation, and by the grant 2831.2003.09 of the State support of young Russian scientists.