2015/02/02 by Dhroova Aiylam, Tanya Khovanova, Aiylam, Dhroova +1
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Number Theory (math.NT) #Rough Sets and Fuzzy Logic #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1502.00682
openalex publication_date 2015/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.