Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions
Number Theory
2008-12-17 v2 Combinatorics
Abstract
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 with integer distances to the origin equal 2, 3, 4 ... The faces are considered up to the action of the group of integer-linear transformations. In conclusion we formulate some actual unsolved problems associated with the generalizations for n-dimensional faces and more complicated face configurations.
Cite
@article{arxiv.math/0510482,
title = {Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions},
author = {Oleg Karpenkov},
journal= {arXiv preprint arXiv:math/0510482},
year = {2008}
}
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