Enumeration problems of oriented serial sequences

The sets of $n$-valued $m$-sequences of a serial structure are considered. In addition to the conventional concepts of length of a series and the number of series in a sequence, the concepts of height of a series and series heights sequence are introduced. The structure of the sequences that are called oriented is determined from limitations on the number and the length of series, on order of sequencing of series of various heights.
A general approach to solving enumeration problems for sets of such sequences is proposed. It is based on formulas for the number of arrangements of elements in cells and the power of a set of height sequences. Exact solutions for some limitations which are important applications are obtained.