Enumeration of integral tetrahedra

URN to cite this document: urn:nbn:de:bvb:703-opus-4275

Title data

Kurz, Sascha:
Enumeration of integral tetrahedra.
Bayreuth , 2007

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Name:	tetrahedrons_ar.pdf
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Abstract

We determine the numbers of integral tetrahedra with diameter d up to isomorphism for all d<=1000 via computer enumeration. Therefore we give an algorithm that enumerates the integral tetrahedra with diameter at most d in O(d^5) time and an algorithm that can check the canonicity of a given integral tetrahedron with at most 6 integer comparisons. For the number of isomorphism classes of integral 4x4 matrices with diameter d fulfilling the triangle inequalities we derive an exact formula.

Abstract in another language

Wir bestimmen die Anzahl ganzzahliger Tetraeder mit Durchmesser d bis auf Isomorphie für alle d kleiner gleich 1000. Der zugrunde liegende Algorithmus hat eine Zeitkomplexität von O(d^5) und basiert auf impliziter Erzeugung.

Further data

Item Type:	Preprint, postprint
Additional notes (visible to public):	msc: 33F05
Keywords:	Geometrische Kombinatorik; Geometrische Wahrscheinlichkeit; Tetraeder; ganzzahlige tetraeder; ordnungstreues Erzeugen; geometrische Wahrscheinlichkeit; implicit enumeration; integral tetrahedra; geometric probability; Euclidean metric; orderly generation; canonicity check
DDC Subjects:	500 Science > 510 Mathematics
Institutions of the University:	Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics > Chair Mathematical Economics - Univ.-Prof. Dr. Jörg Rambau Faculties Faculties > Faculty of Mathematics, Physics und Computer Science
Language:	English
Originates at UBT:	Yes
URN:	urn:nbn:de:bvb:703-opus-4275
Date Deposited:	25 Apr 2014 11:23
Last Modified:	27 Mar 2019 13:14
URI:	https://epub.uni-bayreuth.de/id/eprint/654

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