Enumeration problems for oriented serial sequences

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