Related papers: Consistency of multidimensional combinatorial subs…
A combinatorial substitution is a map over tilings which allows to define sets of tilings with a strong hierarchical structure. In this paper, we show that such sets of tilings are sofic, that is, can be enforced by finitely many local…
An important question in dynamical systems is the classification problem, i.e., the ability to distinguish between two isomorphic systems. In this work, we study the topological factors between a family of multidimensional substitutive…
Given a text and a pattern over two types of symbols called constants and variables, the parameterized pattern matching problem is to find all occurrences of substrings of the text that the pattern matches by substituting a variable in the…
We study the diagonals of two-dimensional tilings generated by direct product substitutions. The properties of these diagonals are primarily determined by the eigenvalues of the substitution matrix, but also the order of the letters in the…
We generalize the notion of (geometric) substitution rule to obtain overlapping substitutions. Our motivating example is the substitution presented in Ziherl, Dotera and Bekku \cite{DBZ}, which features a substitution matrix with…
Hypersubstitutions are mappings which map operation symbols to terms. Terms can be visualized by trees. Hypersubstitutions can be extended to mappings defined on sets of trees. The nodes of the trees, describing terms, are labelled by…
Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…
The theory of substitution sequences and their higher-dimensional analogues is intimately connected with symbolic dynamics. By systematically studying the factors (in the sense of dynamical systems theory) of a substitution dynamical…
We consider the problem of deciding whether a highly incomplete signal lies within a given subspace. This problem, Matched Subspace Detection, is a classical, well-studied problem when the signal is completely observed. High- dimensional…
Tilings and point sets arising from substitutions are classical mathematical models of quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding spectral questions tied to the underlying measures and…
Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…
Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…
Multidimensional Consistency becomes more and more important in the theory of discrete integrable systems. Recently, we gave a classification of all 3D consistent 6-tuples of equations with the tetrahedron property, where several novel…
Multidimensional persistence studies topological features of shapes by analyzing the lower level sets of vector-valued functions. The rank invariant completely determines the multidimensional analogue of persistent homology groups. We prove…
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.…
This paper is intended to provide an introduction to the theory of substitution tilings. For our purposes, tiling substitution rules are divided into two broad classes: geometric and combinatorial. Geometric substitution tilings include…
Since some years, non-overlapping sets of strings (also called cross-bifix-free sets) have had an increasing interest in the frame of the researches about Theory of Codes. Recently some non-overlapping sets of strings with variable length…
This paper describes an alternative method of generating fixed points of certain substitution systems. This method centres on taking infinite words consisting of one repeated letter per word. These infinite words are then interlaced to form…
We present a criterion, based on three commutator relations, that allows to decide whether two self-adjoint matrices with non-overlapping support are simultaneously unitarily similar to quasidiagonal matrices, i.e., whether they can be…
Given a combinatorial structure, a ``twin'' is a pair of disjoint substructures which are isomorphic (or look the same in some sense). In recent years, there have been many problems about finding large twins in various combinatorial…