Geodesic
On the structure of graph of polynomial transformation of the Galois ring
Matematičeskie voprosy kriptografii, Tome 6 (2015) no. 3, pp. 47-73 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Graphs of polynomial transformations of Galois ring $R$ having cardinality $q^n$ and characteristic $p^n$ are studied. A cyclic structure of polynomial permutations having maximal possible cycle length $q(q-1)p^{n-2}$ is described and an algorithm for the construction of such permutations is proposed. For graphs of nonbijective transformations some numerical characteristics of sets of noncyclic vertices are computed. 
@article{MVK_2015_6_3_a3,
     author = {D. M. Ermilov and O. A. Kozlitin},
     title = {On the structure of graph of polynomial transformation of the {Galois} ring},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {47--73},
     year = {2015},
     volume = {6},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2015_6_3_a3/}
}
TY  - JOUR
AU  - D. M. Ermilov
AU  - O. A. Kozlitin
TI  - On the structure of graph of polynomial transformation of the Galois ring
JO  - Matematičeskie voprosy kriptografii
PY  - 2015
SP  - 47
EP  - 73
VL  - 6
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MVK_2015_6_3_a3/
LA  - ru
ID  - MVK_2015_6_3_a3
ER  - 
%0 Journal Article
%A D. M. Ermilov
%A O. A. Kozlitin
%T On the structure of graph of polynomial transformation of the Galois ring
%J Matematičeskie voprosy kriptografii
%D 2015
%P 47-73
%V 6
%N 3
%U http://geodesic.mathdoc.fr/item/MVK_2015_6_3_a3/
%G ru
%F MVK_2015_6_3_a3
D. M. Ermilov; O. A. Kozlitin. On the structure of graph of polynomial transformation of the Galois ring. Matematičeskie voprosy kriptografii, Tome 6 (2015) no. 3, pp. 47-73. http://geodesic.mathdoc.fr/item/MVK_2015_6_3_a3/

[1] Glukhov M. M., Elizarov V. P., Nechaev A. A., Algebra, Gelios-ARV, M., 2003, 749 pp.

[2] Carlitz L., “Functions and polynomials ($\operatorname{mod}\,p^n$)”, Acta Arithmetica, 9 (1964), 66–78 | MR

[3] Knut D. E., Iskusstvo programmirovaniya, v. 2, Izd. dom Vilyams, Moskva–Sankt-Peterburg–Kiev, 2000, 828 pp.

[4] Anashin V. S., “O gruppakh i koltsakh, obladayuschikh tranzitivnymi polinomami”, XVI Vsesoyuznaya algebraicheskaya konferentsiya, Tezisy, ch. II, 1981, 4–5

[5] Larin M. V., “Tranzitivnye polinomialnye preobrazovaniya kolets vychetov”, Diskretn. matem., 14:2 (2002), 20–32 | DOI | MR | Zbl

[6] Nechaev A. A., “Polinomialnye preobrazovaniya konechnykh kommutativnykh kolets glavnykh idealov”, Matematicheskie zametki, 27:6 (1980), 885–897 | MR | Zbl

[7] Viktorenkov V. E., “Orgraf polinomialnogo preobrazovaniya nad kommutativnym lokalnym koltsom”, Obozr. prikl. i promyshl. matem., 7:2 (2000), 327

[8] Viktorenkov V. E., “O nekotorykh kharakteristikakh tsiklovoi struktury sluchainykh ravnoveroyatnykh podstanovok s pomechennymi tsiklami i ikh primenenie dlya issledovaniya polinomialnykh preobrazovanii kolets”, Obozr. prikl. i promyshl. matem., 10:3 (2003), 621

[9] Ermilov D. M., Kozlitin O. A., “Tsiklovaya struktura polinomialnogo generatora nad koltsom Galua”, Matematicheskie voprosy kriptografii, 4:1 (2013), 27–57

[10] Elizarov V. P., Konechnye koltsa, Gelios-ARV, M., 2006, 304 pp.

[11] Asanov M. O., Baranskii V. A., Rasin V. V., Diskretnaya matematika: grafy, matroidy, algoritmy, NITs Regulyarnaya i khaoticheskaya dinamika, Izhevsk, 2001, 288 pp.