The MAX-MIN tiling problem is as follows. We are given A[1, . . . , n][1, . . . , n], a two-dimensional array where each entry A[i][j ] stores a non-negative number. Define a tile of A to be a subarray A[ , . . . , r][t, . . . , b] of A, the weight of a tile to be the sum of all array entries in it, and a tiling of A to be a collection of tiles of A such that each entry A[i][j ] is contained in...

Anderson and Putnam showed that the cohomology of a substitution tiling space may be computed by collaring tiles to obtain a substitution which “forces its border.” One can then represent the tiling space as an inverse limit of an inflation and substitution map on a cellular complex formed from the collared tiles; the cohomology of the tiling space is computed as the direct limit of the homomor...

In this paper, we introduce a practical modeling approach to improve the quality of polygonal mesh structures. Our approach is based on a discrete version of Gaussian-Bonnet theorem on piecewise planar manifold meshes and vertex angle deflections that determines local geometric behavior. Based on discrete GaussianBonnet theorem, summation of angle deflections of all vertices is independent of m...

In this paper we consider higher order infinitesimal bending of a surface in E3. Sufficient condition for a toroid generated by polygonal meridian to be non-rigid of higher order is given. This work is an extension of the results [1]-[7]. Examples of non-rigid surfaces, with visual presentation of infinitesimal bending are given. AMS Subj. Class.: 53A05, 53C45, 68U05

Abstract A recent paper of Balogh, Li and Treglown [3] initiated the study Dirac-type problems for ordered graphs. In this paper, we prove a number results in area. particular, determine asymptotically minimum degree threshold forcing (i) perfect H -tiling an graph, any fixed graph interval chromatic at least $3$ ; (ii) G covering proportion vertices (for ); (iii) -cover ). The first two these ...

We study some decision problems concerning the tiling of the plane with Wang tiles We present a proof for the undecidability of the tiling problem for the whole plane and also for the periodic tiling In these poofs an aperiodic tile set is constructed We are interested in the second part in the link between the cardinality of possible tilings of the plane with a given tile set and the existence...

Linear algebra codes contain data locality which can be exploited by tiling multiple loop nests. Several approaches to tiling have been suggested for avoiding connict misses in low associativity caches. We propose a new technique based on intra-variable padding and compare its performance with existing techniques. Results show padding improves performance of matrix multiply by over 100% in some...

We describe a weakly mixing 1-dimensional tiling dynamical system in which the tiling space is modeled by a surface M of genus 2. The tiling system satis es an in ation, and the in ation map is modeled by a pseudo-Anosov di eomorphism D on M . The expansion coe cient for D is a non-Pisot number. In particular, the leaves of the expanding foliation for D are tiled by their visits to the elements...

In this paper I have settled the open problem, posed by J. Marshall Ash and S. Golomb in [4], of tiling an m × n rectangle with L-shaped trominoes, with the condition that 3 |(mn 2) and a domino is removed from the given rectangle. It turns out that for any given m, n ≥ 7, the only pairs of squares which prevent a tiling are {(1,2), (2,2)}, {(2,1), (2,2)}, {(2,3), (2,4)}, {(3,2), (4,2)} and the...