TY - JOUR

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

N1 - Publisher Copyright:
© 2017, University of Waterloo. All rights reserved.

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

VL - 20

JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

IS - 1

M1 - 17.1.7

ER -