TL;DR
This paper introduces Farey Recursive Functions, exploring their properties and connections to the Farey graph, with applications in the study of 2-bridge knots and links.
Contribution
It defines a new class of recursive functions based on the Farey graph and investigates their fundamental properties and applications in knot theory.
Findings
Farey Recursive Functions are well-defined and exhibit specific recursive properties.
These functions have natural applications in the study of 2-bridge knots and links.
The paper establishes foundational properties linking Farey graphs and recursive functions.
Abstract
This paper introduces Farey Recursive Functions and investigates their basic properties. Farey Recursive Functions are a special type of recursive function from the rationals to a commutative ring. The recursion of these functions is organized by the Farey graph. They arise naturally in the study of 2-bridge knots and links.
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