The homology group of a tiling introduced by M. Reid is studied for certain topological tilings. As in the planar case, finite square grids on surfaces, method groups, namely non-triviality some specific element allows "coloring proof" impossibility tiling. Several results about non-existence polyomino tilings square-tiled surfaces are proved paper.

The stress wave propagation in a generalized thermoelastic polygonal plate of inner and outer cross sections is studied using the Fourier expansion collocation method. The wave equation of motion based on two-dimensional theory of elasticity is applied under the plane strain assumption of generalized thermoelastic plate of polygonal shape, composed of homogeneous isotropic material.  The freque...

We present results connecting the shape of the numerical range to intrinsic properties of a matrix A. When A is a nonnegative matrix, these results are to a large extent analogous to the Perron-Frobenius theory, especially as it pertains to irreducibility and cyclicity in the combinatorial sense. Special attention is given to polygonal, circular and elliptic numerical ranges. The main vehicles ...

Tiling is a well-known loop transformation, which is basically used to expose coarse-grain parallelism and to exploit data reuse at the cache level. However, it can also be used to exploit data reuse at the register level and to improve programs's ILP. Previous work on tiling and also commercial compilers are able to perform tiling for the register level in more than one dimension when the iter...

We look at sets of tiles that can tile any region of size greater than 1 on the square grid. This is not the typical tiling question, but relates closely to it and therefore can help solve other tiling problems – we give an example of this. We also present a result to a more classic tiling question with dominoes and L-shape tiles.

This paper aims at discussing the polynomial approach to the problem of tiling the (musical) time axis with translates of one tile. This mathematical construction naturally leads to a new family of rhythmic tiling canons having the property of being generated by cyclotomic polynomials (tiling cyclotomic canons).

We investigate the dynamics of substitution subshifts and their associated tiling spaces. For a given subshift, the associated tiling spaces are all homeomorphic, but their dynamical properties may differ. We give criteria for such a tiling space to be weakly mixing, and for the dynamics of two such spaces to be topologically conjugate.

We introduce the 2-dimensional square Fibonacci tiling and its generalization to higher dimensions as models for quasicrystals without ‘forbidden’ symmetries. We derive some of the basic mathematical properties of the tiling as well as calculate its diffraction pattern. We discuss the relevance of the Fibonacci tiling for quasicrystal research and for applications in other fields.  2002 Elsevi...

Tiling is a useful loop transformation for expressing parallelism and data locality. Automated tiling transformations that preserve data-locality are increasingly important due to hardware trends towards massive parallelism and the increasing costs of data movement relative to the cost of computing. We propose TiDA as a durable tiling abstraction that centralizes parameterized tiling informatio...