Related papers: Self-dual tilings with respect to star-duality
A notion of dual curve for pseudoholomorphic curves in 4--manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with,…
In this paper we give a classification of tilings of the sphere by congruent quadrilaterals with exactly two equal edges. The tilings are the earth map tilings, $(p,q)$-earth map tilings and their flip modifications, and quadrilateral…
A new method for constructing self-referential tilings of Euclidean space from a graph directed iterated function system, based on a combinatorial structure we call a pre-tree, is introduced. In the special case that we refer to as…
We show that the self-duality defined in [Trautman, Int.J.Theor.Phys.,{\bf 16},561 (1977)] is equivalent to strong self-duality defined in [Bilge, Dereli and Kocak, Lett.Math.Phys., {\bf 36}, 301-309, (1996)] and we obtain an upper bound on…
Penrose limits of inhomogeneous cosmologies admitting two abelian Killing vectors and their abelian T-duals are found in general. The wave profiles of the resulting plane waves are given for particular solutions. Abelian and non-abelian…
A self-affine tiling of a compact set G of positive Lebesgue measure is its partition to parallel shifts of a compact set which is affinely similar to G. We find all polyhedral sets (unions of finitely many convex polyhedra) that admit…
An h-tiling on a finite simplicial complex is a partition of its geometric realization by maximal simplices deprived of several codimension one faces together with possibly their remaining face of highest codimension. In this last case, the…
Orthogonal projections of the uniform measure on the Sierpinski triangle form a family of self similar measures with overlaps. The main result of this work is to make a connection between the dimension theory of these measures and the…
We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as…
The edge-to-edge tilings of the sphere by congruent polygons, where all edges are straight, have been completely classified. We classify the curvilinear version of the similar triangular tilings, where the edges may not be straight, and…
We describe topological gauge theories for which duality properties are encoded by construction. We study them for compact manifolds of dimensions four, eight and two. The fields and their duals are treated symmetrically, within the context…
We consider a certain tiling problem of a planar region in which there are no long horizontal or vertical strips consisting of copies of the same tile. Intuitively speaking, we would like to create a dappled pattern with two or more kinds…
We give a construction of a self-similar tiling of the plane with any prescribed expansion coefficient $\lambda\in\C$ (satisfying the necessary algebraic condition of being a complex Perron number). For any integer $m>1$ we show that there…
Every simple quadrangulation of the sphere is generated by a graph called a pseudo-double wheel with two local expansions (Brinkmann et al. "Generation of simple quadrangulations of the sphere." Discrete Math., Vol. 305, No. 1-3, pp. 33-54,…
We establish a structure theorem for the family of Ammann A2 tilings of the plane. Using that theorem we show that every Ammann A2 tiling is self-similar in the sense of [B. Solomyak, Nonperiodicity implies unique composition for…
n this article, firstly, we introduce the notion of star modules with respect to a balanced pair and obtain some properties. We mainly give the relationship between n-X star modules and n-X tilting modules [9], and a new characterization of…
A variant of the topological twist, involving SL(2,Z) dualities and hence named topological duality twist, is introduced and explicitly applied to describe a U(1) N=4 super Yang-Mills theory on a Kaehler space with holomorphically…
Tile \(\mathbb{R}^2\) into disjoint unit squares \(\{S_k\}_{k \geq 0}\) with the origin being the centre of \(S_0\) and say that \(S_i\) and \(S_j\) are star adjacent if they share a corner and plus adjacent if they share an edge. Every…
Starting from a generalization of a recent result on self-duality we systematically analyze self-dual models. We find a criterion to judge whether a given model is self-dual or not. With this tool we construct some new self-dual pairs,…
The vertex corona of a vertex of some tiling is the vertex together with the adjacent tiles. A tiling where all vertex coronae are congruent is called monocoronal. We provide a classification of monocoronal tilings in the Euclidean plane…