Farey recursive functions

Eric Chesebro; Cory Emlen; Kenton Ke; Denise Lafontaine; Kelly McKinnie; Catherine Rigby

doi:10.2140/involve.2021.14.439

Farey recursive functions

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

Mathematics

University of Montana

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	439-461
Number of pages	23
Journal	Involve
Volume	14
Issue number	3
DOIs	https://doi.org/10.2140/involve.2021.14.439
State	Published - 2021

Keywords

2-bridge knot
2-bridge link
Farey graph
Recursion

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10.2140/involve.2021.14.439

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title = "Farey recursive functions",

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.",

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AU - Chesebro, Eric

AU - Emlen, Cory

AU - Ke, Kenton

AU - Lafontaine, Denise

AU - McKinnie, Kelly

AU - Rigby, Catherine

PY - 2021

Y1 - 2021

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AB - 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.

KW - 2-bridge knot

KW - 2-bridge link

KW - Farey graph

KW - Recursion

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DO - 10.2140/involve.2021.14.439

M3 - Article

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SN - 1944-4176

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EP - 461

JO - Involve

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Farey recursive functions

Abstract

Keywords

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