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

V. A. Amelkin

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk

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 a difference in heights of the neighboring series in the case when this difference lies between $\delta_1$ and $\delta_2$ are examined.
Formulas for powers of these sets and algorithms for the direct and reverse numerations (assigning smaller numbers to the lexicographically lower-order sequences or smaller numbers to the lexicographically higher-order sequences) are obtained.

Key words: serial sequences, series length, series height, constraints.

UDC: 519.115

Received: 06.09.2011

 English version: Numerical Analysis and Applications, 2013, 6:3, 177–186

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