The number of distinct and repeated squares and cubes in the Fibonacci sequence

Huang, Yuke; Zhou, Wen

doi:10.48550/arxiv.1603.04211

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction2

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2016

Publication Types

Select...

Other3

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using these properties, we determined the number of palindromes (resp. k-th powers of words) occurring in F [1, n] (the prefix of F of length n) and T [1, n] for all n ≥ 1, see [8,9,10]. These topics are of great importance in computer science.…”

Section: Introductionmentioning

confidence: 99%

Envelope Words and Return Words Sequences in the Period-doubling Sequence

Yuke,

Zhiying

2016

Preprint

View full text Add to dashboard Cite

We consider the infinite one-sided sequence generated by the period-doubling substitution σ(a, b) = (ab, aa), denoted by D. Since D is uniformly recurrent, each factor ω appears infinite many times in the sequence, which is arranged as ω p (p ≥ 1). Let r p (ω) be the p-th return word over ω. The main result is: for each factor ω, the sequence {r p (ω)} p≥1 is Θ 1 or Θ 2 , which are substitutive sequences and determined completely in this paper.

show abstract

Section: Introductionmentioning

confidence: 99%

Envelope Words and Return Words Sequences in the Period-doubling Sequence

Yuke,

Zhiying

2016

Preprint

View full text Add to dashboard Cite

show abstract

“…In this paper, for all n, m ≥ 1, we give: (1) explicit expressions of A(n), C(n), B(t m ) and D(t m ); (2) fast algorithms for counting B(n) and D(n). We also considered this problem in the Fibonacci sequence, see [4].…”

Section: Introductionmentioning

confidence: 99%

The numbers of distinct and repeated squares and cubes in the Tribonacci sequence

Huang¹,

Zhou²

2016

Preprint

View full text Add to dashboard Cite

The Tribonacci sequence T is the fixed point of the substitution σ(a, b, c) = (ab, ac, a). The main result is twofold: (1) we give the explicit expressions of the numbers of distinct squares and cubes in T[1, n] (the prefix of T of length n); (2) we give algorithms for counting the number of repeated squares and cubes in T[1, n] for all n; then get explicit expressions for some special n such as n = t m (the Tribonacci number).

show abstract

The Numbers of Distinct Squares and Cubes in the Tribonacci Sequence

Huang¹,

Zhou²

2016

Preprint

View full text Add to dashboard Cite

The number of distinct and repeated squares and cubes in the Fibonacci sequence

Cited by 3 publications

References 7 publications

Envelope Words and Return Words Sequences in the Period-doubling Sequence

Envelope Words and Return Words Sequences in the Period-doubling Sequence

The numbers of distinct and repeated squares and cubes in the Tribonacci sequence

The Numbers of Distinct Squares and Cubes in the Tribonacci Sequence

Contact Info

Product

Resources

About