Vol. 14, No. 3, 2021

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Farey recursive functions

Eric Chesebro, Cory Emlen, Kenton Ke, Denise LaFontaine, Kelly McKinnie and Catherine Rigby

Vol. 14 (2021), No. 3, 439–461
Abstract

We introduce Farey recursive functions and investigate 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.

Keywords
recursion, Farey graph, 2-bridge link, 2-bridge knot
Mathematical Subject Classification
Primary: 57M50
Secondary: 05A10
Milestones
Received: 9 September 2020
Revised: 7 January 2021
Accepted: 23 January 2021
Published: 17 July 2021

Communicated by Colin Adams
Authors
Eric Chesebro
Department of Mathematical Sciences
University of Montana
Missoula, MT
United States
Cory Emlen
Department of Mathematical Sciences
University of Montana
Missoula, MT
United States
Kenton Ke
Department of Mathematical Sciences
University of Montana
Missoula, MT
United States
Denise LaFontaine
Department of Mathematical Sciences
University of Montana
Missoula, MT
United States
Kelly McKinnie
Department of Mathematical Sciences
University of Montana
Missoula, MT
United States
Catherine Rigby
Department of Mathematical Sciences
University of Montana
Missoula, MT
United States