Closed Ziv–Lempel factorization of the m-bonacci words

Jahannia, Marieh; Noori, Morteza Mohammad; Rampersad, Narad; Stipulanti, Manon

doi:10.1016/j.tcs.2022.03.019

Cited by 5 publications

(4 citation statements)

References 22 publications

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“…Since their introduction, there has been much research into the properties of closed and privileged words [1,2,4,6,12,16,17,20]. One problem that has received some interest lately [7,14,18,19] is to find good upper and lower bounds for the number of closed and privileged words.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Bounds for the Number of Closed and Privileged Words

Gabrić

2024

Electron. J. Combin.

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A word $w$ has a border $u$ if $u$ is a non-empty proper prefix and suffix of $u$. A word $w$ is said to be closed if $w$ is of length at most $1$ or if $w$ has a border that occurs exactly twice in $w$. A word $w$ is said to be privileged if $w$ is of length at most $1$ or if $w$ has a privileged border that occurs exactly twice in $w$. Let $C_k(n)$ (resp. $P_k(n)$) be the number of length $n$ closed (resp. privileged) words over a $k$-letter alphabet. In this paper, we improve existing upper and lower bounds on $C_k(n)$ and $P_k(n)$. We completely resolve the asymptotic behaviour of $C_k(n)$. We also nearly completely resolve the asymptotic behaviour of $P_k(n)$ by giving a family of upper and lower bounds that are separated by a factor that grows arbitrarily slowly.

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Section: Introductionmentioning

confidence: 99%

Asymptotic Bounds for the Number of Closed and Privileged Words

Gabrić

2024

Electron. J. Combin.

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“…It is recognized that the tribonacci sequence augments the classical Fibonacci sequence from its binary form to a three-letter configuration. Beyond this, extensions involving k letters gave birth to the k-bonacci sequence, a topic that has witnessed rigorous explorations [9][10][11]. Notably, recent contributions by Ghareghani, Mohammad-Noori, and Sharifani [12,13] presented a broadened scope by generalizing the k-bonacci sequence to an infinite alphabet.…”

Section: Introductionmentioning

confidence: 99%

Kernel Words and Gap Sequences of the Tribonacci Word on an Infinite Alphabet

Zhang

2023

Mathematics

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“…Břinda, Pelantová and Turek [18] gave the extension of the Fibonacci sequence to an alphabet of m letters, which is called m-bonacci sequence. Jahannia, Mohammad-Noori, Rampersad and Stipulanti [19,20] studied the Ziv-Lempel factorization of m-bonacci words. Recently, Zhang, Wen and Wu [21] gave the extension of the Fibonacci sequence to the infinite alphabet N and studied its combinatorial properties, including the growth order, digit sum and several decompositions.…”

Section: Introductionmentioning

confidence: 99%