Avoiding conjugacy classes on the 5-letter alphabet

Badkobeh, Golnaz; Ochem, Pascal

doi:10.1051/ita/2020003

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Algebraic Interpretation Of Lie Complexity1

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2021

2022

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Cited by 2 publications

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“…, x d } be a finite alphabet and we let w be a right-infinite word over Σ. (2) We let A w be the factor algebra of w with base field k = Q. Notice that since V n has a basis given by factors of w of length n, we have…”

Section: Algebraic Interpretation Of Lie Complexitymentioning

confidence: 99%

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Lie complexity of words

Bell,

Shallit

2021

Preprint

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Given a finite alphabet Σ and a right-infinite word w over Σ, we define the Lie complexity function Lw : N → N, whose value at n is the number of conjugacy classes (under cyclic shift) of length-n factors x of w with the property that every element of the conjugacy class appears in w.We show that the Lie complexity function is uniformly bounded for words with linear factor complexity, and as a result we show that words of linear factor complexity have at most finitely many primitive factors y with the property that y n is again a factor for every n.We then look at automatic sequences and show that the Lie complexity function of a k-automatic sequence is again k-automatic.

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Section: Algebraic Interpretation Of Lie Complexitymentioning

confidence: 99%

“…The preceding example gives a word in which every factor of length at least two has some cyclic conjugate that is not a factor. Badkobeh and Ochem [2] give an example of such a word over a 5-letter alphabet. In general, the property that L w (n) = 0 for n ≥ i has been studied over various alphabets [14].…”

Section: Examplesmentioning

confidence: 99%