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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
External document link
http://arxiv.org/abs/math/0510482v2
Date
2007
Journal name
Monatshefte für Mathematik
Volume
152
Number
3
Publisher
Springer
Pages
217-249
Publication identifier
Metadata
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Author(s)
Karpenkov, Oleg
Abstract (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.
Subjects / Keywords
Convex polygons; integer lattices; multidimensional continued fractions