Stern-Brocot Trees from Weighted Mediants

Abstract

In this paper we discuss a natural generalization of the Stern Brocot tree which comes from the introduction of weighted mediants. We focus our attention on the case $k=3$, in which $(2a+c)/(2b+d)$ and $(a+2c)/(b+2d)$ are the two mediants inserted between $a/b$ and $c/d$. Our main result is a determination of which rational numbers between the starting terms appear in the tree. We extend this result to arbitrary reduction schemes as well.

13 pages

References in corpus (2)

• Regularity properties of the Stern enumeration of the rationals
• Modified Stern-Brocot Sequences

Cited by in corpus (1)

• Weighted Mediants and Fractals