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

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dc.creatorKarpenkov, Oleg
dc.date2005-10-22
dc.date2006-12-12
dc.date.accessioned2026-07-07T12:13:24Z
dc.date.available2026-07-07T12:13:24Z
dc.descriptionIn 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.
dc.descriptionMinor changes
dc.identifierhttps://arxiv.org/abs/math/0510482
dc.identifierhttp://arxiv.org/abs/math/0510482
dc.identifierMonatshefte fuer Mathematik, vol.152, pp.217-249, 2007.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210834
dc.subjectNumber Theory
dc.subjectCombinatorics
dc.subject11H06; 52C07
dc.titleCompletely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions
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