Related papers: Palindromic sequences generated from marked morphi…
A \emph{morphism} is a mapping that transforms words through letter-wise substitution, where each symbol is consistently replaced by a fixed word. In the field of combinatorics on words, one topic that has attracted considerable attention…
A simple Parry number is a real number \beta>1 such that the R\'enyi expansion of 1 is finite, of the form d_\beta(1)=t_1...t_m. We study the palindromic structure of infinite aperiodic words u_\beta that are the fixed point of a…
We show that the number of length-n words over a k-letter alphabet having no even palindromic prefix is the same as the number of length-n unbordered words, by constructing an explicit bijection between the two sets. A slightly different…
We study infinite words fixed by a morphism and their derived words. A derived word is a coding of return words to a factor. We exhibit two examples of sets of morphisms which are closed under derivation --- any derived word with respect to…
We study algorithmic complexity and expressive power of fusion grammars, a novel formalism introduced in [Kreowski, Kuske, and Lye 2017], which extends hyperedge replacement grammars. In the first part of the work, we prove that the…
Prefix normal words are binary words in which each prefix has at least the same number of $\so$s as any factor of the same length. Firstly introduced by Fici and Lipt\'ak in 2011, the problem of determining the index of the prefix…
Indices of fixed point classes play a central role in Nielsen fixed point theory. Jiang-Wang-Zhang proved that for selfmaps of graphs and surfaces, the index of any fixed point class has an upper bound called its characteristic. In this…
The palindromization map $\psi$ in a free monoid $A^*$ was introduced in 1997 by the first author in the case of a binary alphabet $A$, and later extended by other authors to arbitrary alphabets. Acting on infinite words, $\psi$ generates…
Parikh-collinear morphisms have the property that all the Parikh vectors of the images of letters are collinear, i.e., the associated adjacency matrix has rank 1. In the conference DLT-WORDS 2023 we showed that fixed points of…
A finite word $w$ of length $n$ contains at most $n+1$ distinct palindromic factors. If the bound $n+1$ is attained, the word $w$ is called rich. An infinite word $w$ is called rich if every finite factor of $w$ is rich. Let $w$ be a word…
Recently, a new characterization of Lyndon words that are also perfectly clustering was proposed by Lapointe and Reutenauer (2024). A word over a ternary alphabet {a,b,c} is called perfectly clustering Lyndon if and only if it is the…
Let A be a finite alphabet and f: A^* --> A^* be a morphism with an iterative fixed point f^\omega(\alpha), where \alpha{} is in A. Consider the subshift (X, T), where X is the shift orbit closure of f^\omega(\alpha) and T: X --> X is the…
Trapezoidal words are words having at most $n+1$ distinct factors of length $n$ for every $n\ge 0$. They therefore encompass finite Sturmian words. We give combinatorial characterizations of trapezoidal words and exhibit a formula for their…
Two words are $k$-binomially equivalent if each subword of length at most $k$ occurs the same number of times in both words. The $k$-binomial complexity of an infinite word is a counting function that maps $n$ to the number of $k$-binomial…
In [X. Droubay et al, Episturmian words and some constructions of de Luca and Rauzy, Theoret. Comput. Sci. 255 (2001)], it was proved that every word w has at most |w|+1 many distinct palindromic factors, including the empty word. The…
mu-constant families of holomorphic function germs with isolated singularities are considered from a global perspective. First, a monodromy group from all families which contain a fixed singularity is studied. It consists of automorphisms…
In 2013, Fici and Zamboni proved a number of theorems about finite and infinite words having only a small number of factors that are palindromes. In this paper we rederive some of their results, and obtain some new ones, by a different…
The prefix palindromic length $\mathrm{PPL}_{\mathbf{u}}(n)$ of an infinite word $\mathbf{u}$ is the minimal number of concatenated palindromes needed to express the prefix of length $n$ of $\mathbf{u}$. Since 2013, it is still unknown if…
We extend the classical Ostrowski numeration systems, closely related to Sturmian words, by allowing a wider range of coefficients, so that possible representations of a number $n$ better reflect the structure of the associated Sturmian…
We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories,…