Compression theorems for periodic tilings and consequences.
Convex Polytopes Whose Projection Bodies and Difference Sets Are Polars.
Counting fixed-height tatami tilings.
Covering a Square by Small Perimeter Rectangles.
Covering the Plane with Convex Polygons.
Cube tilings as contributions of algebra to geometry.
Cube-Tilings of Rn and Nonlinear Codes.
Curvature flows of maximal integral triangulations
This paper describes local configurations of some planar triangulations. A Gauss-Bonnet-like formula holds locally for a kind of discrete “curvature” associated to such triangulations.
Decomposition of Convex Figures into Similar Pieces.
Dihedral -tilings of the sphere by rhombi and triangles.
Dihedral f-tilings of the sphere by spherical triangles and equiangular well-centered quadrangles.
Dissections of Regular Polygons into Triangles of Equal Areas.
Distinct equilateral triangle dissections of convex regions
We define a proper triangulation to be a dissection of an integer sided equilateral triangle into smaller, integer sided equilateral triangles such that no point is the vertex of more than three of the smaller triangles. In this paper we establish necessary and sufficient conditions for a proper triangulation of a convex region to exist. Moreover we establish precisely when at least two such equilateral triangle dissections exist. We also provide necessary and sufficient conditions for some convex...
Divisible tilings in the hyperbolic plane.
Domino tilings and products of Fibonacci and Pell numbers.
El diámetro de ciertos digrafos circulantes de triple paso.
This paper studies some diameter-related properties of the 3-step circulant digraphs with set of vertices V≡ZN and steps (± a,b). More precisely, it concentrates upon maximizing their order N for any fixed value of their diameter k. In the proposed geometrical approach, each digraph is fully represented by a T-shape tile which tessellates periodically the plane. The study of these tiles leads to the optimal solutions.
Enumeration of tilings of diamonds and hexagons with defects.
Factoring an odd abelian group by lacunary cyclic subsets
It is a known result that if a finite abelian group of odd order is a direct product of lacunary cyclic subsets, then at least one of the factors must be a subgroup. The paper gives an elementary proof that does not rely on characters.
Factorization results with combinatorial proofs.
Filling a box with translates of two bricks.