Some Structures arising from the Farey Fractal
Number Theory
2026-03-24 v3 Combinatorics
Abstract
This work explores new arithmetic and combinatorial structures arising from the interplay between Farey-type graphs, Fibonacci expansions, and operadic constructions. We introduce Fibonadic numbers, defined as an inverse limit under the Zeckendorf shift, equipped with a metric, order, and commutative rig structure.
Keywords
Cite
@article{arxiv.2509.10959,
title = {Some Structures arising from the Farey Fractal},
author = {Shai Haran},
journal= {arXiv preprint arXiv:2509.10959},
year = {2026}
}