Circular critical exponents for Thue–Morse factors

Shallit, Jeffrey; Zarifi, Ramin

doi:10.1051/ita/2018008

Cited by 6 publications

(3 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark 3. We can combine these automata, as in [6], to get a single DFAO that, on input (i, n), computes which of the six possibilities in Theorem 1 occurs. However, the resulting automaton has 30 states and is rather complicated in appearance, so we don't give it here.…”

Section: Automatamentioning

confidence: 99%

Intertwining of Complementary Thue-Morse Factors

Shallit¹

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Automatamentioning

confidence: 99%

Intertwining of Complementary Thue-Morse Factors

Shallit¹

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…We wish to keep the discussion on the decision procedure and usage of Walnut brief, so we merely describe the logical formulas necessary to encode our problem and refer the reader to [8] for a proof of Theorem 5.3 using Walnut. See also [34].…”

Section: Theorem 53 If N /mentioning

confidence: 99%

Avoiding abelian powers cyclically

Peltomäki,

Whiteland

2020

Preprint

View full text Add to dashboard Cite

We study a new notion of cyclic avoidance of abelian powers. A finite word w avoids abelian N-powers cyclically if for each abelian N-power of period m occurring in the infinite word w ω , we have m ≥ |w|. Let A(k) be the least integer N such that for all n there exists a word of length n over a k-letter alphabet that avoids abelian N-powers cyclically. Let A ∞ (k) be the least integer N such that there exist arbitrarily long words over a k-letter alphabet that avoid abelian N-powers cyclically.We prove that 5 ≤ A(2) ≤ 8, 3 ≤ A(3) ≤ 4, 2 ≤ A(4) ≤ 3, and A(k) = 2 for k ≥ 5. Moreover, we show that A ∞ (2) = 4, A ∞ (3) = 3, and A ∞ (4) = 2.

show abstract

“…Proof. We can use the ideas in [11], adapted for our case. We create first-order logical predicates crep, facge2, and circsf as follows:…”

Section: Circularly Squarefree Ternary Words Via Walnutmentioning

confidence: 99%

Circularly Squarefree Words and Unbordered Conjugates: A New Approach

Clokie

Gabric

Shallit

2019

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Using a new approach based on automatic sequences, logic, and a decision procedure, we reprove some old theorems about circularly squarefree words and unbordered conjugates in a new and simpler way. Furthermore, we prove three new results about unbordered conjugates: we complete the classification, due to Harju and Nowotka, of binary words with the maximum number of unbordered conjugates; we prove that for every possible number, up to the maximum, there exists a word having that number of unbordered conjugates, and finally, we determine the expected number of unbordered conjugates in a random word.

show abstract

Circular critical exponents for Thue–Morse factors

Abstract: We prove various results about the largest exponent of a repetition in a factor of the Thue-Morse word, when that factor is considered as a circular word. Our results confirm and generalize previous results of Fitzpatrick and Aberkane & Currie.

Cited by 6 publications

References 7 publications

Intertwining of Complementary Thue-Morse Factors

Intertwining of Complementary Thue-Morse Factors

Avoiding abelian powers cyclically

Circularly Squarefree Words and Unbordered Conjugates: A New Approach

Contact Info

Product

Resources

About