Related papers: Burrows-Wheeler transformations and de Bruijn word…
We define generalized de Bruijn words as those words having a Burrows-Wheeler transform that is a concatenation of permutations of the alphabet. We show that generalized de Bruijn words are in 1-to-1 correspondence with Hamiltonian cycles…
We relate the Burrows-Wheeler transformation with a result in combinatorics on words known as the Gessel-Reutenauer transformation.
The Burrows-Wheeler Transform is a string transformation that plays a fundamental role for the design of self-indexing compressed data structures. Over the years, researchers have successfully extended this transformation outside the…
One of the most well-known variants of the Burrows-Wheeler transform (BWT) [Burrows and Wheeler, 1994] is the bijective BWT (BBWT) [Gil and Scott, arXiv 2012], which applies the extended BWT (EBWT) [Mantaci et al., TCS 2007] to the multiset…
The Burrows-Wheeler transform (BWT) is a permutation whose applications are prevalent in data compression and text indexing. The bijective BWT (BBWT) is a bijective variant of it. Although it is known that the BWT can be constructed in…
This paper initiates the study of shortening universal cycles (u-cycles) and universal words (u-words) for permutations either by using incomparable elements, or by using non-deterministic symbols. The latter approach is similar in nature…
A word over an ordered alphabet is said to be clustering if identical letters appear adjacently in its Burrows-Wheeler transform. Such words are strictly related to (discrete) interval exchange transformations. We use an extended version of…
We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets of patterns. In some cases we employ the graph of pattern…
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…
Given a string of characters, the Burrows-Wheeler Transform rearranges the characters in it so as to produce another string of the same length which is more amenable to compression techniques such as move to front, run-length encoding, and…
The Burrows-Wheeler Transform (BWT) is a word transformation introduced in 1994 for Data Compression. It has become a fundamental tool for designing self-indexing data structures, with important applications in several area in science and…
The Burrows-Wheeler Transform (BWT) is a fundamental component in many data structures for text indexing and compression, widely used in areas such as bioinformatics and information retrieval. The extended BWT (eBWT) generalizes the…
The recently introduced class of Wheeler graphs, inspired by the Burrows-Wheeler Transform (BWT) of a given string, admits an efficient index data structure for searching for subpaths with a given path label, and lifts the applicability of…
The Burrows-Wheeler transform (BWT) is a reversible transform that converts a string $w$ into another string $\mathsf{BWT}(w)$. The size of the run-length encoded BWT (RLBWT) can be interpreted as a measure of repetitiveness in the class of…
In this paper we study the number $r_{bwt}$ of equal-letter runs produced by the Burrows-Wheeler transform ($BWT$) when it is applied to purely morphic finite words, which are words generated by iterating prolongable morphisms. Such a…
We study the cycle structure of words in several random permutations. We assume that the permutations are independent and that their distribution is conjugation invariant, with a good control on their short cycles. If, after successive…
We characterize the clustering of a word under the Burrows-Wheeler transform in terms of the resolution of a bounded number of bispecial factors belonging to the language generated by all its powers. We use this criterion to compute, in…
The sort transform (ST) is a modification of the Burrows-Wheeler transform (BWT). Both transformations map an arbitrary word of length n to a pair consisting of a word of length n and an index between 1 and n. The BWT sorts all rotation…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
The Burrows-Wheeler Transform (BWT) of a string is an invertible permutation of the string, which can be used for data compression and compact indexes for string pattern matching. Ganguly et al. [SODA, 2017] introduced the parameterized BWT…