KERNEL WORDS AND GAP SEQUENCE OF THE TRIBONACCI SEQUENCE

doi:10.1016/S0252-9602(15)30086-2

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (1): 173-194.doi: 10.1016/S0252-9602(15)30086-2

KERNEL WORDS AND GAP SEQUENCE OF THE TRIBONACCI SEQUENCE

黄煜可¹, 文志英²

1. School of Mathematics and Systems Science, Beihang University, Beijing 100191, China;
2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

收稿日期:2014-10-11 修回日期:2015-03-04 出版日期:2016-01-30 发布日期:2016-01-30
通讯作者: Zhiying WEN,E-mail:wenzy@tsinghua.edu.cn E-mail:wenzy@tsinghua.edu.cn
作者简介:Yuke HUANG,E-mail:hyg03ster@163.com
基金资助:
The work described in this paper was supported by grants from the National Science Foundation of China(11431007; 11271223; 11371210).

KERNEL WORDS AND GAP SEQUENCE OF THE TRIBONACCI SEQUENCE

Yuke HUANG¹, Zhiying WEN²

1. School of Mathematics and Systems Science, Beihang University, Beijing 100191, China;
2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received:2014-10-11 Revised:2015-03-04 Online:2016-01-30 Published:2016-01-30
Contact: Zhiying WEN,E-mail:wenzy@tsinghua.edu.cn E-mail:wenzy@tsinghua.edu.cn
Supported by:
The work described in this paper was supported by grants from the National Science Foundation of China(11431007; 11271223; 11371210).

摘要/Abstract

摘要：

In this paper, we investigate the factor properties and gap sequence of the Tri-bonacci sequence, the fixed point of the substitution σ(a, b, c)=(ab, ac, a). Let ω_p be the p-th occurrence of ω and G_p(ω) be the gap between ω_p and ω_p+1. We introduce a notion of kernel for each factor ω, and then give the decomposition of the factor ω with respect to its kernel. Using the kernel and the decomposition, we prove the main result of this paper:for each factor ω, the gap sequence {G_p(ω)}_p≥1 is the Tribonacci sequence over the alphabet {G₁(ω), G₂(ω), G₄(ω)}, and the expressions of gaps are determined completely. As an appli-cation, for each factor ω and p∈N, we determine the position of ω_p. Finally we introduce a notion of spectrum for studying some typical combinatorial properties, such as power, overlap and separate of factors.

关键词: the Tribonacci sequence, gap sequence, kernel word, combinatorial property, spectrum

Abstract:

Key words: the Tribonacci sequence, gap sequence, kernel word, combinatorial property, spectrum

中图分类号:

11B85

黄煜可, 文志英. KERNEL WORDS AND GAP SEQUENCE OF THE TRIBONACCI SEQUENCE[J]. 数学物理学报(英文版), 2016, 36(1): 173-194.

Yuke HUANG, Zhiying WEN. KERNEL WORDS AND GAP SEQUENCE OF THE TRIBONACCI SEQUENCE[J]. Acta mathematica scientia,Series B, 2016, 36(1): 173-194.

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KERNEL WORDS AND GAP SEQUENCE OF THE TRIBONACCI SEQUENCE

KERNEL WORDS AND GAP SEQUENCE OF THE TRIBONACCI SEQUENCE

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