Related papers: Multidimensional Shifts And Finite Matrices

Domino tilings have been studied extensively for both their statistical properties and their dynamical properties. We construct a subshift of finite type using matching rules for several types of dominos. We combine the previous results…

Finite dimensional (FD) models, i.e., deterministic functions of time/space and finite sets of random variables, are constructed for target vector-valued random processes/fields. They are required to have two properties. First, standard…

For a given metric measure space $(X,d,\mu)$ we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS)…

In this paper we will look at the connection of frames and finite dimensionality. A main focus is to present simple algorithms and make them available online. The main result is a way to 'switch' between different frames, giving an…

We define the finite extension property for $d$-dimensional subshifts, which generalizes the topological strong spatial mixing condition defined by Brice\~no (2016), and we prove that this property is invariant under topological conjugacy.…

The scope of this paper is two-fold. First, to present to the researchers in combinatorics an interesting implementation of permutations avoiding generalized patterns in the framework of discrete-time dynamical systems. Indeed, the orbits…

This paper introduces the concept of a generating set for stochastic matrices -- a subset of matrices whose repeated composition generates the entire set. Understanding such generating sets requires specifying the "indivisible elements" and…

We investigate how embedding dimension affects the emergence of an internal "world model" in a transformer trained with reinforcement learning to perform bubble-sort-style adjacent swaps. Models achieve high accuracy even with very small…

New low-order $H(\textrm{div})$-conforming finite elements for symmetric tensors are constructed in arbitrary dimension. The space of shape functions is defined by enriching the symmetric quadratic polynomial space with the $(d+1)$-order…

Let ${\mathcal P}\subset{\mathbb Z}^2$ be a convex polygon with each vertex in it labeled by an element from a finite set and such that the labeling of each vertex $v\in {\mathcal P}$ is uniquely determined by the labeling of all other…

Let $(X,d)$ be a finite metric space with $|X|=n$. For a positive integer $k$ we define $A_k(X)$ to be the quotient set of all $k$-subsets of $X$ by isometry, and we denote $|A_k(X)|$ by $a_k$. The sequence $(a_1,a_2,\ldots,a_{n})$ is…

We consider the approximation properties of finite element spaces on quadrilateral meshes. The finite element spaces are constructed starting with a given finite dimensional space of functions on a square reference element, which is then…

We characterize separable multidimensional permutations in terms of forbidden patterns and enumerate them by means of generating function, recursive formula and explicit formula. We find a connection between multidimensional permutations…

Subshifts are sets of colorings of $\mathbb{Z}^d$ defined by families of forbidden patterns. In a given subshift, the extender set of a finite pattern is the set of all its admissible completions. Since soficity of $\mathbb{Z}$ subshifts is…

We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.

The aim of this article is to find appropriate definitions for shifts of finite type and sofic shifts in a general context of symbolic dynamics. We start showing that the classical definitions of shifts of finite type and sofic shifts, as…

The topological properties of a material depend on its symmetries, parameters, and spatial dimension. Changes in these properties due to parameter and symmetry variations can be understood by computing the corresponding topological…

We provide exact and asymptotic formulae for the number of unrestricted, respectively indecomposable, $d$-dimensional matrices where the sum of all matrix entries with one coordinate fixed equals 2.

We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…

We show that the sets of periods of multidimensional shifts of finite type (SFTs) are exactly the sets of integers of the complexity class $\NE$. We also show that the functions counting their number are the functions of #E. We also give…