Some Structures arising from the Farey Fractal

2025/09/13 by Shai Haran, Haran, Shai
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2509.10959

openalex publication_date 2025/09/13 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

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.

Citations

• Meditations on the Farey Fractal

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