Enumeration of integral tetrahedra
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.
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.
| Institutes: | Mathematik |
|---|---|
| Author: | Sascha Kurz |
| Year of Completion: | 2007 |
| SWD-Keyword: | Geometrische Kombinatorik; Geometrische Wahrscheinlichkeit; Tetraeder |
| Tag: | ganzzahlige tetraeder; geometrische Wahrscheinlichkeit; ordnungstreues Erzeugen Euclidean metric; canonicity check; geometric probability; implicit enumeration; integral tetrahedra; orderly generation |
| Dewey Decimal Classification: | 510 Mathematik |
| MSC-Classification: | 33F05 Numerical approximation and evaluation [See also 65D20] |
| URN: | urn:nbn:de:bvb:703-opus-4275 |
| Document Type: | Working Paper |
| Language: | English |
| Date of Publication (online): | 15.04.2008 |
