Cubes of integral vectors in dimension four

Emil W. Kiss, Péter Kutas

Type: Article

Publication Date: 2012-11-17

Citations: 1

DOI: https://doi.org/10.1556/sscmath.49.2012.4.1225

Abstract

A system of m nonzero vectors in ℤ n is called an m -icube if they are pairwise orthogonal and have the same length. The paper describes m -icubes in ℤ 4 for 2 ≦ m ≦ 4 using Hurwitz integral quaternions, counts the number of them with given edge length, and proves that unlimited extension is possible in ℤ 4 .

Locations

Studia Scientiarum Mathematicarum Hungarica - View
ELTE Digital Institutional Repository (EDIT) (Eötvös Loránd University) - View - PDF
arXiv (Cornell University) - View - PDF

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Works Cited by This (8)

Action	Title	Year	Authors
+	Vorlesungen über die Zahlentheorie der Quaternionen	1919	Adolf Hurwitz
+	On Quaternions and Octonions	2003	John H. Conway Derek A. Smith
+ PDF Chat	Sums of squares and orthogonal integral vectors	2011	Lee M. Goswick Emil W. Kiss Gábor Moussong Nándor Simányi
+ PDF Chat	�ber die Komposition der quadratischen Formen	1922	A. Hurwitz
+	Gruppentheoretischer Beweis des Satzes von Hurwitz-Radon über die Komposition quadratischer Formen	1942	Beno Eckmann
+ PDF Chat	An introduction to the theory of numbers	1960	G. H. Hardy
+	An Introduction to the Theory of Numbers. By G. H. Hardy and E. M. Wright. 2nd edition. Pp. xvi, 407 25s. 1945. (Oxford)	1946	T. A. A. B.
+ PDF Chat	An Introduction to the Theory of Numbers	1946	E. C. T.