A generalized family of multidimensional continued fractions: TRIP Maps-Reference-Cited by-同舟云学术

A generalized family of multidimensional continued fractions: TRIP Maps

Published:2014-10-29 Issue:08 Volume:10 Page:2151-2186
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Dasaratha Krishna¹,Flapan Laure²,Garrity Thomas³,Lee Chansoo⁴,Mihaila Cornelia⁵,Neumann-Chun Nicholas³,Peluse Sarah⁶,Stoffregen Matthew²

Affiliation:

1. Department of Mathematics, Stanford University, Stanford, CA 94305, USA

2. Department of Mathematics, University of California at Los Angeles, Los Angeles, CA 90095-1555, USA

3. Department of Mathematics, Williams College, Williamstown, MA 01269, USA

4. Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, MI 48109, USA

5. Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, USA

6. 5343 S. Kimbark Ave. Apt 2, Chicago, IL 60615, USA

Abstract

Most well-known multidimensional continued fractions, including the Mönkemeyer map and the triangle map, are generated by repeatedly subdividing triangles. This paper constructs a family of multidimensional continued fractions by permuting the vertices of these triangles before and after each subdivision. We obtain an even larger class of multidimensional continued fractions by composing the maps in the family. These include the algorithms of Brun, Parry-Daniels and Güting. We give criteria for when multidimensional continued fractions associate sequences to unique points, which allows us to determine when periodicity of the corresponding multidimensional continued fraction corresponds to pairs of real numbers being cubic irrationals in the same number field.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042114500730

Reference14 articles.

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