Stern sequences for a family of multidimensional continued fractions: TRIP-Stern sequences

Ilya Amburg; Krishna Dasaratha; Laure Flapan; Thomas Garrity; Chansoo Lee; Cornelia Mihaila; Nicholas Neumann-Chun; Sarah Peluse; Matthew Stoffregen

Stern sequences for a family of multidimensional continued fractions: TRIP-Stern sequences

Ilya Amburg, Krishna Dasaratha, Laure Flapan, Thomas Garrity, Chansoo Lee, Cornelia Mihaila, Nicholas Neumann-Chun, Sarah Peluse, Matthew Stoffregen

Mathematics

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

4 Scopus citations

Abstract

The Stern diatomic sequence is closely linked to continued fractions via the Gauss map on the unit interval, which in turn can be understood via systematic subdivisions of the unit interval. Higher-dimensional analogues of continued fractions, called multidimensional continued fractions, can be produced through various subdivisions of a triangle. We define triangle partition-Stern sequences (TRIP-Stern sequences for short) from certain triangle divisions developed earlier by the authors. These sequences are higher-dimensional generalizations of the Stern diatomic sequence. We then prove several combinatorial results about TRIP-Stern sequences, many of which give rise to well-known sequences. We finish by generalizing TRIP-Stern sequences and presenting analogous results for these generalizations.

Original language	English (US)
Article number	17.1.7
Journal	Journal of Integer Sequences
Volume	20
Issue number	1
State	Published - Dec 26 2016

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

Keywords

Multidimensional continued fraction
Stern’s diatomic sequence

Cite this

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title = "Stern sequences for a family of multidimensional continued fractions: TRIP-Stern sequences",

abstract = "The Stern diatomic sequence is closely linked to continued fractions via the Gauss map on the unit interval, which in turn can be understood via systematic subdivisions of the unit interval. Higher-dimensional analogues of continued fractions, called multidimensional continued fractions, can be produced through various subdivisions of a triangle. We define triangle partition-Stern sequences (TRIP-Stern sequences for short) from certain triangle divisions developed earlier by the authors. These sequences are higher-dimensional generalizations of the Stern diatomic sequence. We then prove several combinatorial results about TRIP-Stern sequences, many of which give rise to well-known sequences. We finish by generalizing TRIP-Stern sequences and presenting analogous results for these generalizations.",

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T1 - Stern sequences for a family of multidimensional continued fractions

T2 - TRIP-Stern sequences

AU - Amburg, Ilya

AU - Dasaratha, Krishna

AU - Flapan, Laure

AU - Garrity, Thomas

AU - Lee, Chansoo

AU - Mihaila, Cornelia

AU - Neumann-Chun, Nicholas

AU - Peluse, Sarah

AU - Stoffregen, Matthew

PY - 2016/12/26

Y1 - 2016/12/26

N2 - The Stern diatomic sequence is closely linked to continued fractions via the Gauss map on the unit interval, which in turn can be understood via systematic subdivisions of the unit interval. Higher-dimensional analogues of continued fractions, called multidimensional continued fractions, can be produced through various subdivisions of a triangle. We define triangle partition-Stern sequences (TRIP-Stern sequences for short) from certain triangle divisions developed earlier by the authors. These sequences are higher-dimensional generalizations of the Stern diatomic sequence. We then prove several combinatorial results about TRIP-Stern sequences, many of which give rise to well-known sequences. We finish by generalizing TRIP-Stern sequences and presenting analogous results for these generalizations.

AB - The Stern diatomic sequence is closely linked to continued fractions via the Gauss map on the unit interval, which in turn can be understood via systematic subdivisions of the unit interval. Higher-dimensional analogues of continued fractions, called multidimensional continued fractions, can be produced through various subdivisions of a triangle. We define triangle partition-Stern sequences (TRIP-Stern sequences for short) from certain triangle divisions developed earlier by the authors. These sequences are higher-dimensional generalizations of the Stern diatomic sequence. We then prove several combinatorial results about TRIP-Stern sequences, many of which give rise to well-known sequences. We finish by generalizing TRIP-Stern sequences and presenting analogous results for these generalizations.

KW - Multidimensional continued fraction

KW - Stern’s diatomic sequence

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M3 - Article

AN - SCOPUS:85011977260

SN - 1530-7638

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JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

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M1 - 17.1.7

ER -

Stern sequences for a family of multidimensional continued fractions: TRIP-Stern sequences

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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