A generalization of Markov Numbers

Esther Banaian; Archan Sen

doi:10.1007/s11139-023-00801-6

A generalization of Markov Numbers

Esther Banaian^*, Archan Sen

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Abstract

We explore a generalization of the Markov numbers that is motivated by a specific generalized cluster algebra arising from an orbifold, in the sense of Chekhov and Shapiro. We give an explicit algorithm for computing these generalized Markov numbers and exhibit several patterns analogous to those that appear within the ordinary Markov numbers. Along the way, we present formulas related to continued fractions and snake graphs.

Original language	English
Journal	Ramanujan Journal
Volume	63
Issue	4
Pages (from-to)	1021-1055
Number of pages	35
ISSN	1382-4090
DOIs	https://doi.org/10.1007/s11139-023-00801-6
Publication status	Published - Apr 2024

Keywords

Continued fractions
Markov numbers
Triangulated surfaces

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10.1007/s11139-023-00801-6

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title = "A generalization of Markov Numbers",

abstract = "We explore a generalization of the Markov numbers that is motivated by a specific generalized cluster algebra arising from an orbifold, in the sense of Chekhov and Shapiro. We give an explicit algorithm for computing these generalized Markov numbers and exhibit several patterns analogous to those that appear within the ordinary Markov numbers. Along the way, we present formulas related to continued fractions and snake graphs.",

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AU - Sen, Archan

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023.

PY - 2024/4

Y1 - 2024/4

N2 - We explore a generalization of the Markov numbers that is motivated by a specific generalized cluster algebra arising from an orbifold, in the sense of Chekhov and Shapiro. We give an explicit algorithm for computing these generalized Markov numbers and exhibit several patterns analogous to those that appear within the ordinary Markov numbers. Along the way, we present formulas related to continued fractions and snake graphs.

AB - We explore a generalization of the Markov numbers that is motivated by a specific generalized cluster algebra arising from an orbifold, in the sense of Chekhov and Shapiro. We give an explicit algorithm for computing these generalized Markov numbers and exhibit several patterns analogous to those that appear within the ordinary Markov numbers. Along the way, we present formulas related to continued fractions and snake graphs.

KW - Continued fractions

KW - Markov numbers

KW - Triangulated surfaces

U2 - 10.1007/s11139-023-00801-6

DO - 10.1007/s11139-023-00801-6

M3 - Journal article

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VL - 63

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EP - 1055

JO - Ramanujan Journal

JF - Ramanujan Journal

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A generalization of Markov Numbers

Abstract

Keywords

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