Geodesic
A Probabilistic Approach to the Problem of the Defects of Admissible Sets in a Lattice
Matematičeskie zametki, Tome 68 (2000) no. 6, pp. 910-916 
A. M. Raigorodskii. A Probabilistic Approach to the Problem of the Defects of Admissible Sets in a Lattice. Matematičeskie zametki, Tome 68 (2000) no. 6, pp. 910-916. http://geodesic.mathdoc.fr/item/MZM_2000_68_6_a11/
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Voir la notice de l'article provenant de la source Math-Net.Ru

New estimates for the defect of the admissible set in a lattice are obtained for a sufficiently large class of sequences.

[1] Raigorodskii A. M., “Defekt dopustimykh sharov i oktaedrov v reshetke i sistemy obschikh predstavitelei”, Matem. sb., 189:6 (1998), 117–141 | MR | Zbl

[2] Moschevitin N. G., “Defekt dopustimogo oktaedra v reshetke”, Matem. zametki, 58 (1995), 558–568 | MR | Zbl

[3] Cusick T. W., Wolfskill J., “Lattice octahedra and sums of powers of linear forms”, J. London Math. Soc. (2), 38 (1988), 207–215 | DOI | MR | Zbl

[4] Mordell L. J., “Lattice octahedra”, Canad. J. Math., 12 (1960), 297–302 | MR | Zbl

[5] Bantegnie R., “Le problème des octaedres en dimension 5”, Acta Arith., 14 (1968), 185–202 | MR | Zbl

[6] Wessels U., Die Sätze von White und Mordell über kritische Gitter von Polytopen in den Dimensionen 4 und 5, Diplomarbeit, Mathematisches Institut der Ruhr-Universität Bochum, 1989

[7] Ryshkov S. S., “K probleme otyskaniya sovershennykh kvadratichnykh form ot mnogikh peremennykh”, Tr. MIAN, 142, Nauka, M., 1976, 215–239 | MR | Zbl

[8] Zakharova N. V., “Tsentrirovki 8-mernykh reshetok, sokhranyayuschie reper posledovatelnykh minimumov”, Tr. MIAN, 152, Nauka, M., 1980, 97–123 | MR | Zbl

[9] Raigorodskii A. M., “The defects of admissible sets in a lattice, and systems of common representatives”, Grazer Mathematische Berichte, 1999, no. 338, 31–62 | MR | Zbl

[10] Erdesh P., Spenser Dzh., Veroyatnostnye metody v kombinatorike, Mir, M., 1976

[11] Kuzyurin N. N., “Asimptoticheskoe issledovanie zadachi o pokrytii”, Problemy kibernetiki, 1980, no. 37, 19–56 | MR | Zbl

[12] Raigorodskii A. M., “Sistemy obschikh predstavitelei”, Fundament. i prikl. matem., 5:3 (1999), 851–860 | MR | Zbl

[13] Tarakanov V. E., Kombinatornye zadachi i $(0,1)$-matritsy, Fizmatlit, M., 1985 | Zbl

[14] Gruber P. M., Lekkerkerker C. G., Geometry of Numbers, North-Holland, Amsterdam, 1987 | Zbl

[15] Cassels J. W. S., An Introduction to the Geometry of Numbers, Springer-Verlag, Berlin–Göttingen–Heidelberg, 1959 | Zbl

[16] Korobov N. M., Teoretiko-chislovye metody v priblizhennom analize, Fizmatlit, M., 1963