Enumerating the Rationals from Left to Right

Authors

Stephen P. Glasby, Central Washington University

Department or Administrative Unit

Mathematics

Document Type

Article

Author Copyright

© The Mathematical Association of America

Publication Date

11-2011

Journal

The American Mathematical Monthly

Abstract

The rationals can be enumerated using Stern-Brocot sequences SB_n, Calkin-Wilfsequences CW_n, or Farey sequences F_n. We show that the rationals in SB_n, CW^_n, and F_n canbe computed using very similar second-order linear recurrence relations. (This, incidentally,obviates the need to compute previous sequences SB_i, CW_i, F_i with i

Comments

This article was originally published in The American Mathematical Monthly. The full-text article from the publisher can be found here.

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Recommended Citation

Glasby, S. P. (2011). Enumerating the Rationals from Left to Right. The American Mathematical Monthly, 118(9), 830. https://doi.org/10.4169/amer.math.monthly.118.09.830