Geodesic
Algorithms for enumeration and numeration coding of sequences with specified lengths of maximal series
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 5 (2002) no. 3, pp. 215-223.

Voir la notice de l'article provenant de la source Math-Net.Ru

Sets of binary and $n$-valued sequences of length $m$ with specified limitations on lengths of maximal series are considered. Exact formulas for the determination of powers of such sets have been obtained. Algorithms of numeration coding and generation for binary sequences have been obtained. 
@article{SJVM_2002_5_3_a1,
     author = {V. A. Amelkin},
     title = {Algorithms for enumeration and numeration coding of sequences with specified lengths of maximal series},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {215--223},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2002_5_3_a1/}
}
TY  - JOUR
AU  - V. A. Amelkin
TI  - Algorithms for enumeration and numeration coding of sequences with specified lengths of maximal series
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2002
SP  - 215
EP  - 223
VL  - 5
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2002_5_3_a1/
LA  - ru
ID  - SJVM_2002_5_3_a1
ER  - 
%0 Journal Article
%A V. A. Amelkin
%T Algorithms for enumeration and numeration coding of sequences with specified lengths of maximal series
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2002
%P 215-223
%V 5
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2002_5_3_a1/
%G ru
%F SJVM_2002_5_3_a1
V. A. Amelkin. Algorithms for enumeration and numeration coding of sequences with specified lengths of maximal series. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 5 (2002) no. 3, pp. 215-223. http://geodesic.mathdoc.fr/item/SJVM_2002_5_3_a1/

[1] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, Nauka, M., 1982 | MR | Zbl

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

[3] Goncharov V. L., “Iz oblasti kombinatoriki”, Izv. AN SSSR. Ser. mat., 8:1 (1944), 3–48

[4] Trunov A. N., “Predelnye raspredeleniya v zadache o razmeschenii odinakovykh chastits po razlichnym yacheikam”, Veroyatnostnye zadachi diskretnoi matematiki, Trudy Mat. instituta AN SSSR, 177, Nauka, M., 1986, 147–164 | MR

[5] Novak S. Yu., “Asimptoticheskie razlozheniya v zadache o maksimume dlin serii “uspekhov” v markovskoi tsepi s dvumya sostoyaniyami”, Asimptoticheskii analiz raspredelenii sluchainykh protsessov, Trudy IM SO AN SSSR, 13, Nauka, Novosibirsk, 1989, 136–147

[6] Novak S. Yu., “Longest runs in a sequence of m-dependent random variables”, Probab. Theory Related Fields, 91:3/4 (1992), 269–281 | DOI | MR | Zbl

[7] Savelev L. Ya., “Maksimum dlin serii v obobschennykh posledovatelnostyakh Bernulli”, Diskretnaya matematika, 11:1 (1999), 29–52 | MR

[8] Korshunov A. D., “Ob asimptotike chisla binarnykh slov s zadannoi dlinoi maksimalnoi serii. 1”, Diskretnyi analiz i issledovanie operatsii, 4:4 (1997), 13–46 | MR | Zbl

[9] Kostochka A. V., Mazurov V. D., Savelev L. Ya., “Chislo $q$-ichnykh slov s ogranicheniyami na dlinu maksimalnoi serii”, Diskretnaya matematika, 10:1 (1998), 10–19

[10] Amelkin V. A., Algoritmy perechisleniya, kodirovaniya i generirovaniya seriinykh posledovatelnostei s zadannymi dlinami maksimalnykh (minimalnykh) serii, Preprint RAN. Sib. otd-nie. IVMiMG; 1149, Novosibirsk, 2000

[11] Amelkin V. A., “Algoritmy tochnogo resheniya zadach perechisleniya, kodirovaniya i generirovaniya seriinykh posledovatelnostei”, Sib. zhurn. vychis. matematiki / RAN. Sib. otd-nie. — Novosibirsk, 4:1 (2001), 1–12 | MR

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