Enumeration problems of sets of increasing and decreasing n-valued serial sequences with double-ended constraints on series heights

Abstract

Enumeration problems for n-valued serial sequences are considered. Sets of increasing and decreasing sequences whose structure is specified by constraints on lengths of series and on the difference in heights of the neighboring series in the case when this difference lies between δ1 and δ2 are examined. Formulas for powers of these sets and algorithms for the direct and reverse numerations (assigning smaller numbers to lexicographically lower order sequences or smaller numbers to lexicographically higher order sequences) are obtained.