Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-25T08:56:38.553Z Has data issue: false hasContentIssue false
  • English
  • Français

Lattice Tetrahedra

Published online by Cambridge University Press:  20 November 2018

G. K. White
G. K. White*
Affiliation:
University of Toronto and University of British Columbia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A class of problems in the geometry of numbers, for which there are but fragmentary results, may be expressed in general terms, as follows. Let 5 be a given point-set and let G be a given discrete point-set, both in Euclidean n-space. Suppose that Λ is a lattice which contains G but no point of S not in G. Such lattices, if they exist, will be said to be admissible for S with respect to G, and the general problem is to investigate their properties and, if possible, classify them.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 389 - 396
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Bantegnie, R., A propos d'un problème de Mordell sur les octaèdres latticiels, J. London Math. Soc, 37 (1962), 320–328.Google Scholar
2. Briïnngràber, E., Über Punktgitter (Dissertation, Wien, 1944).Google Scholar
3. Minkowski, H., Gesammelte Abhandlungen, Bd. II (Leipzig, 1911).Google Scholar
4. Mordell, L. J., Lattice octahedra, Can. J. Math., 12 (1960), 297–302.Google Scholar
5. Wolff, K. H., Über kritische Gitter im vierdimensionalen Raum, Monatsh. Math., 58 (1954), 38–56.Google Scholar