Related papers: Cyclotomic Aperiodic Substitution Tilings
We use the subgraph replacement method to investigate new properties of the tilings of regions on the square lattice with diagonals drawn in. In particular, we show that the centrally symmetric tilings of a generalization of the Aztec…
Symmetry-protected topological (SPT) phases exhibit nontrivial order if symmetry is respected but are adiabatically connected to the trivial product phase if symmetry is not respected. However, unlike the symmetry-breaking phase, there is…
We present a technique for the enumeration of all isotopically distinct ways of tiling a hyperbolic surface of finite genus, possibly nonorientable and with punctures and boundary. This provides a generalization of the enumeration of…
For a fairly general class of two-dimensional tiling substitutions, we prove that if the length expansion $\beta$ is a Pisot number, then the tilings defined by the substitution must be locally finite. We also give a simple example of a…
We study the tiling of a two-dimensional region of the plane by $K$-cell one-dimensional tiles, or $K$-mers. Unlike previous studies, which typically allowed for one single value of $K$ or sometimes a small assortment of fixed values, here…
This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general…
We consider substitution tilings and Delone sets without the assumption of finite local complexity (FLC). We first give a sufficient condition for tiling dynamical systems to be uniquely ergodic and a formula for the measure of cylinder…
Given a nonnegative matrix $A$, can you find diagonal matrices $D_1,~D_2$ such that $D_1AD_2$ is doubly stochastic? The answer to this question is known as Sinkhorn's theorem. It has been proved with a wide variety of methods, each…
We study a family of substitution tilings with similar right triangles of two sizes which is obtained using the substitution rule introduced in [Danzer, L. and van Ophuysen, G. A species of planar triangular tilings with inflation factor…
The cyclic sieving phenomenon (CSP) provides valuable data about symmetry classes of cyclic actions, and has applications to representation theory. In this paper, we enumerate domino tableaux of shape 2-by-n, and use this result to prove a…
Spatial transcriptomics (ST) is a promising technique that characterizes the spatial gene profiling patterns within the tissue context. Comprehensive ST analysis depends on consecutive slices for 3D spatial insights, whereas the missing…
The design of isophoric phased arrays composed of two-sized square-shaped tiles that fully cover rectangular apertures is dealt with. The number and the positions of the tiles within the array aperture are optimized to fit desired…
Conformal field theories (CFTs) with MN and tetragonal global symmetry in $d=2+1$ dimensions are relevant for structural, antiferromagnetic and helimagnetic phase transitions in a wide class of materials. The study of these theories with…
Association Schemes and coherent configurations (and the related Bose-Mesner algebra and coherent algebras) are well known in combinatorics with many applications. In the 1990s, Mesner and Bhattacharya introduced a three-dimensional…
Crystallographic tilings of the Euclidean space $\mathbb{E}^n$ are defined as simple tilings whose group of isometric automorphisms is crystallographic. To classify crystallographic tilings by their automorphism groups it is necessary to…
A combinatorial tiling of the sphere is naturally given by an embedded graph. We study the case that each tile has exactly five edges, with the ultimate goal of classifying combinatorial tilings of the sphere by geometrically congruent…
We provide combinatorial models for all Kirillov--Reshetikhin crystals of nonexceptional type, which were recently shown to exist. For types D_n^(1), B_n^(1), A_{2n-1}^(2) we rely on a previous construction using the Dynkin diagram…
We consider the triangular lattice ice model (20-Vertex model) with four types of domain-wall type boundary conditions. In types 1 and 2, the configurations are shown to be equinumerous to the quarter-turn symmetric domino tilings of an…
We propose a diagnostic tool for detecting non-trivial symmetry protected topological (SPT) phases protected by a symmetry group $G$ in 2+1 dimensions. Our method is based on directly studying the 1+1-dimensional anomalous edge conformal…
Recent advancements in generalized symmetries have drawn significant attention to gapped phases of matter exhibiting novel symmetries, such as noninvertible symmetries. By leveraging the duality transformations, the classification and…