Geodesic
Enumeration problems of sets of increasing and decreasing $n$-valued serial sequences with double-ended constraints on series heights
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 3, pp. 205-215 
V. A. Amelkin. Enumeration problems of sets of increasing and decreasing $n$-valued serial sequences with double-ended constraints on series heights. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 3, pp. 205-215. http://geodesic.mathdoc.fr/item/SJVM_2013_16_3_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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[2] Amelkin V. A., “Numeratsiya neubyvayuschikh i nevozrastayuschikh seriinykh posledovatelnostei”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 12:4 (2009), 389–401

[3] Cover T. M., “Enumerative source encoding”, IEEE Trans. Inform. Theory, 19:1 (1973), 73–77 | DOI | MR | Zbl

[4] Amelkin V. A., Metody numeratsionnogo kodirovaniya, Nauka, Novosibirsk, 1986 | MR