Numeration of non-decreasing and non-increasing serial sequences

Abstract

Finite sets of n-valued serial sequences are examined. Their structure is determined not only by restrictions on the number of series and series lengths, but also by restrictions on the series heights, which define the order number of series and their lengths, but also is limited to the series heights, by whose limitations the order of series of different heights is given. Solutions to numeration and generation problems are obtained for the following sets of sequences: non-decreasing and non-increasing sequences where the difference in heights of the neighboring series is either not smaller than a certain value or not greater than a certain value. Algorithms that assign smaller numbers to lexicographically lower sequences and smaller numbers to lexicographically higher sequences are developed.