The 2-dimensional Stern-Brocot tree, and the n-dimensional

Speaker: Professor emeritus Håkan Lennerstad, BTH

Venue: C413A
Language: English
Format: The first 15 minutes of this talk are intended for a wide audience. After a short break for questions, the following 30 minutes are intended for mathematics researchers.

Abstract:
In the Stern-Brocot tree all relatively prime pairs of integers are generated iteratively, each is the sum of two other pairs. The tree was discovered in the 1860s, and has found many applications in different areas of mathematics and later in computer science, security systems, statistical control and even music theory.

I will present the n-dimensional Stern-Brocot tree, published 2019, where each relatively prime n-tuple is generated iteratively as the sum of a certain set of relatively prime n-tuples of the previous generation – this is the set of parents. It turns out that only in dimension 2 all n-tuples have the same number of parents. The talk will touch upon generalized Euclidean algorithms, Isomorphisms of trees, matrix representations, Fibonacci type n-tuples, multidimensional continued fractions and combinatorial properties of the trees.

Link to the paper