The goal of this talk is to study the properties of some specific morphic sequences, famously related to beta representations and Dumont-Thomas numeration systems. We show that, using the underlying numeration system, we are able to give explicit string attractors of these sequences.
The aim of the poster is to showcase the interplay between group theory, algebraic topology and combinatorics on words. A result that allows to display this is the return theorem by Berté et al. in 2015. The poster will contain an introduction to fundamental groups of graphs, dendric words as well as a new result concerning return groups of eventua...
Since 2015, dendric shifts (a generalisation of Sturmian words) have been widely studied. One of the results concerning these shift spaces is the return theorem. It describes the groups generated by the return words of a dendric shift. The proof uses the fundamental group of the Rauzy graph of the shift space. Later, eventually dendric shifts were ...
Given an infinite sequence of symbols (called letters) x, with each pattern w appearing in x, we can associate an extension graph. This graph is a bipartite graph describing the letters that we can see to the left and to the right of w in x. If this graph is a tree, then we say that w is dendric. And if it is the case for all w, we say that x itsel...
In this talk, I present the results from the paper of the same name. It is divided in two parts. First, I study the evolution of complexity when applying a morphism to an eventually dendric words. In the second part, I focus on the morphism that preserve dendricity for all dendric words and show that they are obtained as compositions of Arnoux-Rauz...
Given a language L, we associate to each word its extension graph in L. This graph describes the letters that we can see to the left and to the right of the word in L. If this graph is a tree, then we say that the word is dendric, and if all the elements of L are dendric, we say that L itself is dendric. This notion generalizes the well-studied Stu...
The zero-error channel capacity is the maximum asymptotic rate that can be reached with error probability exactly zero, instead of a vanishing error probability. The nature of this problem, essentially combinatorial rather than probabilistic, has led to various researches both in Information Theory and Combinatorics. However, the zero-error capacit...
A word is quasiperiodic (or coverable) if it can be covered with occurrences of another finite word, called its quasiperiod. A word is multi-scale quasiperiodic (or multi-scale coverable) if it has infinitely many different quasiperiods. These notions were previously studied in the domains of text algorithms and combinatorics of right infinite word...
Dagstuhl Seminar 19241 ("25 Years of the Burrows-Wheeler Transform") took place from June 10th to 14th, 2019, and was attended by 45 people from 13 countries and the three fields of Algorithms and Data Structures, Bioinformatics, and Combinatorics on Words. There were four talks and a panel session for each field. Feedback was generally positive an...
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 domains of strings. However, efforts to find non-trivial alternatives of the original, now 25 years old, Burrows-Whe...
