Abelian combinatorics on words: A survey

Fici, Gabriele; Puzynina, Svetlana

doi:10.1016/j.cosrev.2022.100532

Cited by 9 publications

(4 citation statements)

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“…Fici and Puzynina have recently published a comprehensive survey on abelian combinatorics on words [14].…”

Section: Preliminariesmentioning

confidence: 99%

2-balanced sequences coding rectangle exchange transformation

Dvořáková,

Masáková,

Pelantová

2024

Preprint

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We define a new class of ternary sequences that are 2-balanced. These sequencesare obtained by colouring of Sturmian sequences. We show that the class containssequences of any given letter frequencies. We provide an upper bound on factorand abelian complexity of these sequences. Using the interpretation by rectangleexchange transformation, we prove that for almost all triples of letter frequencies,the upper bound on factor and abelian complexity is reached. The bound onfactor complexity is given using a number-theoretical function which we computeexplicitly for a class of parameters. MSC Classification: 68R15

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“…Fici and Puzynina have recently published a comprehensive survey on abelian combinatorics on words [14].…”

Section: Preliminariesmentioning

confidence: 99%

2-balanced sequences coding rectangle exchange transformation

Dvořáková,

Masáková,

Pelantová

2024

Preprint

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“…The abelian complexity of an infinite word w is the function that counts the number of non-abelian equivalent factors of length n, for all n. For instance, for n ≥ 1, the ultimately constant word w = 21222222... admits exactly two non abelianequivalent factors of length n: the one which contains 1, and the one written with the letter 2 only. For an introduction to abelian complexity, or, more generally, to abelian combinatorics on words, we refer to the recent survey [FP23].…”

Section: Abelian Complexity Of Hypercubic Billiard Wordsmentioning

confidence: 99%

Minimal Complexities for Infinite Words Written with d Letters

Andrieu,

Vivion

2023

Lecture Notes in Computer Science

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“…As mentioned, there are a number of alternatives. Readers may wish to consult the excellent survey by Fici and Puzynina [21] on Abelian repetitions and related topics.…”

Section: Introductionmentioning

confidence: 99%