Hankel determinants of a Sturmian sequence

Let $ \tau $ be the substitution $ 1\to 101 $ and $ 0\to 1 $ on the alphabet $ \{0, 1\} $. The fixed point of $ \tau $ obtained starting from 1, denoted by $ {\bf{s}} $, is a Sturmian sequence. We first give a characterization of $ {\bf{s}} $ using $ f $-representation. Then we show that the distrib...
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Autor*in:	Haocong Song [verfasserIn] Wen Wu [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	hankel determinants sturmian sequences

Übergeordnetes Werk:	In: AIMS Mathematics - AIMS Press, 2018, 7(2022), 3, Seite 4233-4265
Übergeordnetes Werk:	volume:7 ; year:2022 ; number:3 ; pages:4233-4265

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3934/math.2022235

Katalog-ID:	DOAJ070755310

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520			\|a Let $ \tau $ be the substitution $ 1\to 101 $ and $ 0\to 1 $ on the alphabet $ \{0, 1\} $. The fixed point of $ \tau $ obtained starting from 1, denoted by $ {\bf{s}} $, is a Sturmian sequence. We first give a characterization of $ {\bf{s}} $ using $ f $-representation. Then we show that the distribution of zeros in the determinants induces a partition of integer lattices in the first quadrant. Combining those properties, we give the explicit values of the Hankel determinants $ H_{m, n} $ of $ {\bf{s}} $ for all $ m\ge 0 $ and $ n\ge 1 $.
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callnumber-first	Q - Science
author	Haocong Song
spellingShingle	Haocong Song misc QA1-939 misc hankel determinants misc sturmian sequences misc Mathematics Hankel determinants of a Sturmian sequence
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topic_title	QA1-939 Hankel determinants of a Sturmian sequence hankel determinants sturmian sequences
topic	misc QA1-939 misc hankel determinants misc sturmian sequences misc Mathematics
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title	Hankel determinants of a Sturmian sequence
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title_full	Hankel determinants of a Sturmian sequence
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title_sort	hankel determinants of a sturmian sequence
callnumber	QA1-939
title_auth	Hankel determinants of a Sturmian sequence
abstract	Let $ \tau $ be the substitution $ 1\to 101 $ and $ 0\to 1 $ on the alphabet $ \{0, 1\} $. The fixed point of $ \tau $ obtained starting from 1, denoted by $ {\bf{s}} $, is a Sturmian sequence. We first give a characterization of $ {\bf{s}} $ using $ f $-representation. Then we show that the distribution of zeros in the determinants induces a partition of integer lattices in the first quadrant. Combining those properties, we give the explicit values of the Hankel determinants $ H_{m, n} $ of $ {\bf{s}} $ for all $ m\ge 0 $ and $ n\ge 1 $.
abstractGer	Let $ \tau $ be the substitution $ 1\to 101 $ and $ 0\to 1 $ on the alphabet $ \{0, 1\} $. The fixed point of $ \tau $ obtained starting from 1, denoted by $ {\bf{s}} $, is a Sturmian sequence. We first give a characterization of $ {\bf{s}} $ using $ f $-representation. Then we show that the distribution of zeros in the determinants induces a partition of integer lattices in the first quadrant. Combining those properties, we give the explicit values of the Hankel determinants $ H_{m, n} $ of $ {\bf{s}} $ for all $ m\ge 0 $ and $ n\ge 1 $.
abstract_unstemmed	Let $ \tau $ be the substitution $ 1\to 101 $ and $ 0\to 1 $ on the alphabet $ \{0, 1\} $. The fixed point of $ \tau $ obtained starting from 1, denoted by $ {\bf{s}} $, is a Sturmian sequence. We first give a characterization of $ {\bf{s}} $ using $ f $-representation. Then we show that the distribution of zeros in the determinants induces a partition of integer lattices in the first quadrant. Combining those properties, we give the explicit values of the Hankel determinants $ H_{m, n} $ of $ {\bf{s}} $ for all $ m\ge 0 $ and $ n\ge 1 $.
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title_short	Hankel determinants of a Sturmian sequence
url	https://doi.org/10.3934/math.2022235 https://doaj.org/article/3c1bac6d3f3e4cada2c84fb74c935ed5 https://www.aimspress.com/article/doi/10.3934/math.2022235?viewType=HTML https://doaj.org/toc/2473-6988
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