in the repository
Title data
Kurz, Sascha:
Enumeration of integral tetrahedra.
Bayreuth
,
2007
![[thumbnail of tetrahedrons_ar.pdf]](https://epub.uni-bayreuth.de/style/images/fileicons/application_pdf.png) |
|
||||||||
|
Download (217kB)
|
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): | Erscheint in: Journal of Integer Sequences. Bd. 10 (2007) Heft 9
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: | 15 Jun 2021 08:36 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/654 |
Download Statistics