相关论文: Combinatorial problems of (quasi-)crystallography
We develop a general framework to study hyperuniformity of various mathematical models of quasicrystals. Using this framework we provide examples of non-hyperuniform quasicrystals which unlike previous examples are not limit-quasiperiodic.…
We investigate the use of quasicrystals in image sampling. Quasicrystals produce space-filling, non-periodic point sets that are uniformly discrete and relatively dense, thereby ensuring the sample sites are evenly spread out throughout the…
We propose the theory which unifies the description of quasicrystal assembly thermodynamics and quasicrystal structure formation by combining the Landau theory of crystallization and the cluster approach to quasicrystals. The theory is…
The radial distribution function is a characteristic geometric quantity of a point set in Euclidean space that reflects itself in the corresponding diffraction spectrum and related objects of physical interest. The underlying combinatorial…
We describe a quasiperiodic optical lattice, created by a physical realization of the abstract cut-and-project construction underlying all quasicrystals. The resulting potential is a generalization of the Fibonacci tiling. Calculation of…
In this paper the systematic method of dealing with the arbitrary decorations of quasicrystals is presented. The method is founded on the average unit cell formalism and operates in the physical space only, where each decorating atom…
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
We give a simple computational approach to mathematical quasicrystals, combining cut-and-project methods with self-similarity. Starting with a Pisot unit $\beta$ and an iterated function system $g_k(z)=\beta z +z_k, \ k=1,...,m$ in a…
The centre of the symmetric group algebra $\mathbb{C}[\mathfrak{S}_n]$ has been used successfully for studying important problems in enumerative combinatorics. These include maps in orientable surfaces and ramified covers of the sphere by…
Hyperuniform systems, which include crystals, quasicrystals and special disordered systems, have attracted considerable recent attention, but rigorous analyses of the hyperuniformity of quasicrystals have been lacking because the support of…
The aim of this paper is to study the class of quasicomplemented distributive nearlattices. We investigate $\alpha$-filters and $\alpha$-ideals in quasicomplemented distributive nearlattices and some results on ideals-congruence-kernels.…
The shelling of crystals is concerned with counting the number of atoms on spherical shells of a given radius and a fixed centre. Its straight-forward generalization to quasicrystals, the so-called central shelling, leads to non-universal…
Quasicrystals are unique materials characterized by long-range order without periodicity. They are observed in systems such as metallic alloys, soft matter, and particle simulations. Unlike periodic crystals, which are invariant under…
Regular $A_n$-crystals are certain edge-colored directed graphs which are related to representations of the quantized universal enveloping algebra $U_q(\mathfrak{sl}_{n+1})$. For such a crystal $K$ with colors $1,2,...,n$, we consider its…
Quasicrystals have a higher degree of rotational and point-reflection symmetry than conventional crystals. As a result, quasicrystalline heterostructures fabricated from dielectric materials with micrometer-scale features exhibit…
This mostly expository article explores recent developments in the relations between the three objects in the title from an algebro-combinatorial perspective. We prove a formula for Whittaker functions of a real semisimple group as an…
Relying on rays, we search for submodules of a module V over a supertropical semiring on which a given anisotropic quadratic form is quasilinear. Rays are classes of a certain equivalence relation on V, that carry a notion of convexity,…
A new kind of aperiodic tiling is introduced. It is shown to underlie a structure obtained as a superposition of waves with incommensurate periods. Its connections to other other tilings and quasicrystals are discussed.
The paper describes clustering problems from the combinatorial viewpoint. A brief systemic survey is presented including the following: (i) basic clustering problems (e.g., classification, clustering, sorting, clustering with an order over…
The groups of (linear) similarity and coincidence isometries of certain modules in d-dimensional Euclidean space, which naturally occur in quasicrystallography, are considered. It is shown that the structure of the factor group of…