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Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions

Karpenkov, Oleg (2007), Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions, Monatshefte für Mathematik, 152, 3, p. 217-249. http://dx.doi.org/10.1007/s00605-007-0478-0

Type
Article accepté pour publication ou publié
Lien vers un document non conservé dans cette base
http://arxiv.org/abs/math/0510482v2
Date
2007
Nom de la revue
Monatshefte für Mathematik
Volume
152
Numéro
3
Éditeur
Springer
Pages
217-249
Identifiant publication
Métadonnées
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Auteur(s)
Karpenkov, Oleg
Résumé (EN)
In this paper we develop an integer-affine classification of three-dimensional multistory, completely empty convex marked pyramids. We apply it to obtain the complete lists of compact two-dimensional faces of multidimensional continued fractions lying in planes at integer distances 2, 3, 4, …  to the origin. The faces are considered up to the action of the group of integer-linear transformations.
Mots-clés
Convex polygons; integer lattices; multidimensional continued fractions