Balanced Words Having Simple Burrows-Wheeler Transform

Restivo, Antonio; Rosone, Giovanna

doi:10.1007/978-3-642-02737-6_35

Cited by 5 publications

(4 citation statements)

References 19 publications

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“…From Corollary 3.5 we know that the BWT of T has the shape b x a y . By [42,Thm. 2] for binary words the following conditions are equivalent:…”

Section: Balanced Wordsmentioning

confidence: 99%

On Arithmetically Progressed Suffix Arrays and related Burrows-Wheeler Transforms

Daykin,

Köppl,

Kübel

et al. 2021

Preprint

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We characterize those strings whose suffix arrays are based on arithmetic progressions, in particular, arithmetically progressed permutations where all pairs of successive entries of the permutation have the same difference modulo the respective string length. We show that an arithmetically progressed permutation P coincides with the suffix array of a unary, binary, or ternary string. We further analyze the conditions of a given P under which we can find a uniquely defined string over either a binary or ternary alphabet having P as its suffix array. For the binary case, we show its connection to lower Christoffel words, balanced words, and Fibonacci words. In addition to solving the arithmetically progressed suffix array problem, we give the shape of the Burrows-Wheeler transform of those strings solving this problem. These results give rise to numerous future research directions.

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“…From Corollary 3.5 we know that the BWT of T has the shape b x a y . By [42,Thm. 2] for binary words the following conditions are equivalent:…”

Section: Balanced Wordsmentioning

confidence: 99%

On Arithmetically Progressed Suffix Arrays and related Burrows-Wheeler Transforms

Daykin,

Köppl,

Kübel

et al. 2021

Preprint

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“…There are many results in the literature regarding the occurrence of rich words in infinite and finite words, but there are significantly fewer results about the occurrence of rich words in a language. The occurrence of rich words in the conjugacy class of a word w, denoted by C(w), is a well-studied concept in literature (see [8,12,21,25]). Shallit et al ( [25]) calculated the number of binary words w of a particular length such that every conjugate of w is rich.…”

Section: Introductionmentioning

confidence: 99%

Rich Words in the Block Reversal of a Word

Mahalingam¹,

Maity²,

Pandoh³

2023

Preprint

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The block reversal of a word w, denoted by BR(w), is a generalization of the concept of the reversal of a word, obtained by concatenating the blocks of the word in the reverse order. We characterize non-binary and binary words whose block reversal contains only rich words. We prove that for a binary word w, richness of all elements of BR(w) depends on l(w), the length of the run sequence of w. We show that if all elements of BR(w) are rich, then 2 ≤ l(w) ≤ 8. We also provide the structure of such words.

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“…In particular, standard words -building blocks of infinite Sturmian words -have a BWT of the form b h a j [14]. On a k-letter alphabet, words having a BWT with minimal number of clusters have been characterized in [17] in the case of balanced words, and in [6] in the general case.…”

Section: Introductionmentioning

confidence: 99%

Burrows-Wheeler Transform of Words Defined by Morphisms

Brlek¹,

Frosini

Mancini

et al. 2019

Lecture Notes in Computer Science

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The Burrows-Wheeler transform (BWT) is a popular method used for text compression. It was proved that BWT has optimal performance on standard words, i.e. the building blocks of Sturmian words. In this paper, we study the application of BWT on more general morphic words: the Thue-Morse word and to generalizations of the Fibonacci word to alphabets with more than two letters; then, we study morphisms obtained as composition of the Thue-Morse morphism with a Sturmian one. In all these cases, the BWT efficiently clusters the iterates of the morphisms generating prefixes of these infinite words, for which we determine the compression clustering ratio.

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Balanced Words Having Simple Burrows-Wheeler Transform

Abstract: The investigation of the "clustering effect" of the Burrows-Wheeler transform (BWT) leads to study the words having simple BWT , i.e. words w over an ordered alphabet $A=\{a_1,a_2,\ldots,a_k\}$, with $a_1 < a_2 < \ldots Show more

Cited by 5 publications

References 19 publications

On Arithmetically Progressed Suffix Arrays and related Burrows-Wheeler Transforms

On Arithmetically Progressed Suffix Arrays and related Burrows-Wheeler Transforms

Rich Words in the Block Reversal of a Word

Burrows-Wheeler Transform of Words Defined by Morphisms

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