Related papers: Morphisms preserving the set of words coding three…

We study how much injective morphisms can increase the repetitiveness of a given word. This question has a few possible variations depending on the meaning of ``repetitiveness''. We concentrate on fractional exponents of finite words and…

In the dynamics of a rotation of the unit circle by an irrational angle $\alpha\in(0,1)$, we study the evolution of partitions whose atoms are finite unions of left-closed right-open intervals with endpoints lying on the past trajectory of…

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…

Let E denote the group of all interval exchange transformations on [0,1). Given a suitable topological group structure on E, it is possible to classify all one-parameter interval exchange actions (continuous homomorphisms from R to E). In…

It is shown that, in the variety of ternary rings, the elements of amalgamated free products have unique normal forms, and, moreover, this variety satisfies the strong amalgamation property. Applying these statements, effective codescent…

An infinite permutation is a linear ordering of the set of natural numbers. An infinite permutation can be defined by a sequence of real numbers where only the order of elements is taken into account. In the paper we investigate a new class…

Fixed points ${\bf u}=\varphi({\bf u})$ of marked and primitive morphisms $\varphi$ over arbitrary alphabet are considered. We show that if ${\bf u}$ is palindromic, i.e., its language contains infinitely many palindromes, then some power…

In this paper we consider the following problems: how many different subsets of Sigma^n can occur as set of all length-n factors of a finite word? If a subset is representable, how long a word do we need to represent it? How many such…

A tangram is a word in which every letter occurs an even number of times. Thus it can be cut into parts that can be arranged into two identical words. The \emph{cut number} of a tangram is the minimum number of required cuts in this…

For a positive integer $n$ let $\mathcal{X}_n$ be either the algebra $M_n$ of $n \times n$ complex matrices, the set $N_n$ of all $n \times n$ normal matrices, or any of the matrix Lie groups $\mathrm{GL}(n)$, $\mathrm{SL}(n)$ and…

Let $\Gamma $ be an infinite discrete group and $\mathsf{A}\subset \Gamma $ a nonempty finite subset. The set of permutations $\sigma $ of $\Gamma $ such that $s^{-1}\sigma (s)\in \mathsf{A}$ for every $s\in \Gamma $ can be identified with…

We show that, with the exception of the words $a^2ba^2$ and $b^2ab^2$, all (finite or infinite) binary patterns in the Prouhet-Thue-Morse sequence can actually be found in that sequence as segments (up to exchange of letters in the infinite…

We study the number of linear extensions of a partial order with a given proportion of comparable pairs of elements, and estimate the maximum and minimum possible numbers. We also consider a random interval partial order on $n$ elements,…

Linguistic similarity is multi-faceted. For instance, two words may be similar with respect to semantics, syntax, or morphology inter alia. Continuous word-embeddings have been shown to capture most of these shades of similarity to some…

Let I_n(\pi) denote the number of involutions in the symmetric group S_n which avoid the permutation \pi. We say that two permutations \alpha,\beta\in\S{j} may be exchanged if for every n, k, and ordering \tau of j+1,...,k, we have…

An infinite permutation is a linear ordering of the set of non-negative integers. Generally, the properties of infinite permutations analogous to those of infinite words show some resemblances and some differences between permutations and…

Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We give a general discussion of such models and their rationality criteria. We study exchangeability assessments…

We investigate different notions of recognizability for a free monoid morphism $\sigma: \mathcal{A}^* \to \mathcal{B}^*$. Full recognizability occurs when each (aperiodic) point in $\mathcal{B}^\mathbb{Z}$ admits at most one tiling with…

Words can be represented by composing the representations of subword units such as word segments, characters, and/or character n-grams. While such representations are effective and may capture the morphological regularities of words, they…

A map $f{:}\,[0,1)\to [0,1)$ is a {\it piecewise contraction of $n$ intervals} ($n$-PC) if there exist $0<\lambda<1$ and a partition of $[0,1)$ into intervals $I_1,\ldots,I_n$ such that $f\vert_{I_i}$ is $\lambda$-Lipschitz for every $1\le…