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

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Article number17.1.7
JournalJournal of Integer Sequences
Volume20
Issue number1
StatePublished - Dec 26 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

Keywords

  • Multidimensional continued fraction
  • Stern’s diatomic sequence

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