O jistém pokrytí racionálních bodů v rovině nekonečnou jednoduchou lomenou čarou
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Václav Polák (1960)
Časopis pro pěstování matematiky
Anton Kotzig (1946)
Časopis pro pěstování matematiky a fysiky
Karel Petr (1911)
Časopis pro pěstování mathematiky a fysiky
Christine Bachoc, Gabriele Nebe, Boris Venkov (2002)
Acta Arithmetica
Iskander Aliev (2002)
Acta Arithmetica
Hao Chen (2013)
Journal de Théorie des Nombres de Bordeaux
In this paper we introduce generalized Craig lattices, which allows us to construct lattices in Euclidean spaces of many dimensions in the range which are denser than the densest known Mordell-Weil lattices. Moreover we prove that if there were some nice linear binary codes we could construct lattices even denser in the range . We also construct some dense lattices of dimensions in the range . Finally we also obtain some new lattices of moderate dimensions such as , which are denser than the...
Gilbert Muraz, Jean-Louis Verger-Gaugry (2005)
Journal de Théorie des Nombres de Bordeaux
The set of point sets of , having the property that their minimal interpoint distance is greater than a given strictly positive constant is shown to be equippable by a metric for which it is a compact topological space and such that the Hausdorff metric on the subset of the finite point sets is compatible with the restriction of this topology to . We show that its subsets of Delone sets of given constants in , are compact. Three (classes of) metrics, whose one of crystallographic nature,...
Kołodziejczyk, Krzysztof (1999)
Beiträge zur Algebra und Geometrie
Stefan Kühnlein (1996)
Journal für die reine und angewandte Mathematik
Frédéric Guérin (1991)
Monatshefte für Mathematik
Sándor Szabó (1989)
Aequationes mathematicae
R. Bambah, N. Sloane (1982)
Acta Arithmetica
Michio Ozeki (2011)
Acta Arithmetica
Eskin, Alex, Margulis, Gregory, Mozes, Shahar (1995)
Electronic Research Announcements of the American Mathematical Society [electronic only]
Johannes Schleischitz (2020)
Communications in Mathematics
Following a suggestion of W.M. Schmidt and L. Summerer, we construct a proper -system with the property . In fact, our method generalizes to provide -systems with , for arbitrary . We visualize our constructions with graphics. We further present explicit examples of numbers that induce the -systems in question.
Sukumar Das Adhikari, Yong-Gao Chen (1999)
Acta Arithmetica
Watanabe, Takao (2000)
Journal of Lie Theory
Asmus L. Schmidt (1975)
Mathematische Annalen
Bettina Just, Friedhelm Meyer auf der Heide, Avi Wigderson (1989)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
R. J. Hans-Gill, Madhu Raka, Ranjeet Sehmi (2011)
Acta Arithmetica
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