Hostname: page-component-f554764f5-fnl2l Total loading time: 0 Render date: 2025-04-16T06:16:10.983Z Has data issue: false hasContentIssue false
  • English
  • Français

The Jacobi-Perron algorithm and the algebra of recursive sequences

Published online by Cambridge University Press:  17 April 2009

A.G. Shannon  and
Leon Bernstein
A.G. Shannon
Affiliation:
Department of Applied Mathematics, New South Wales Institute of Technology, Broadway, New South Wales;
Leon Bernstein
Affiliation:
Department of Mathematics, Illinois Institute of Technology, Chicago, Illinois, USA.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper shows the existence of a one-to-one correspondence between a certain class of square matrices of arbitrary order and a related extension field. The elements of these matrices are obtained from certain basic linear recursive sequences by means of a generalization of the euclidean algorithm.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 8 , Issue 2 , April 1973 , pp. 261 - 277
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Bell, E.T., “Notes on recurring series of the third order”, Tôhoku Math. J. 24 (1924), 160–184.Google Scholar
[2]Bernstein, Leon, The Jacobi-Perron algorithm: Its theory and application (Lecture Notes in Mathematics, 207. Springer-Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar
[3]Horadam, A.F., “Generating functions for powers of a certain generalised sequence of numbers”, Duke Math. J. 32 (1965), 437–446.CrossRefGoogle Scholar
[4]Jarden, Dov, Recurring sequences: A collection of papers, 2nd ed. (Riveon Lematematika, Jerusalem, 1966).Google Scholar
[5]MacMahon, Percy A., Combinatorial analysis, Vol. I (Cambridge University Press, Cambridge, 1915).Google Scholar
[6]Ward, Morgan, “The algebra of recurring series”, Ann. of Math. (2) 32 (1931), 1–9.CrossRefGoogle Scholar