Abstract
Sets of n-valued finite serial sequences are investigated. Such a sequence consists of two serial subsequences, beginning with an increasing subsequence and ending in a decreasing one (and vice versa). The structure of these sequences is determined by constraints imposed on the number of series, on series lengths, and on series heights. For sets of sequences the difference between adjacent series heights in which does not exceed a certain given value 1 ≤ |h j+1 − h j | ≤ δ, two algorithms are constructed of which one assigns smaller numbers to lexicographically lower sequences and the other assigns smaller numbers to lexicographically higher sequences.
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Amelkin, V.A., Perechislitel’nye zadachi seriinykh posledovatel’nostei (Enumeration Problems for Serial Sequences), Novosibirsk: Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 2008.
Amelkin, V.A., Enumeration of Nondecreasing and Nonincreasing Serial Sequences, Sib. Zh. Vych. Mat., 2009, vol. 12, no. 4, pp. 389–401.
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Original Russian Text © V.A. Amelkin, 2011, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2011, Vol. 14, No. 2, pp. 119–130.
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Amelkin, V.A. Solutions to enumeration problems for single-transition serial sequences with an adjacent series height increment bounded above. Numer. Analys. Appl. 4, 95–104 (2011). https://doi.org/10.1134/S1995423911020017
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DOI: https://doi.org/10.1134/S1995423911020017