Compression theorems for periodic tilings and consequences.
Displaying 21 – 40 of 116
Convex Polytopes Whose Projection Bodies and Difference Sets Are Polars.
H. Martini (1991)
Discrete & computational geometry
Counting fixed-height tatami tilings.
Ruskey, Frank, Woodcock, Jennifer (2009)
The Electronic Journal of Combinatorics [electronic only]
Covering a Square by Small Perimeter Rectangles.
N. Alon, D.J. Kleitman (1986)
Discrete & computational geometry
Covering the Plane with Convex Polygons.
J. Pach (1986)
Discrete & computational geometry
Cube tilings as contributions of algebra to geometry.
Szabó, Sándor (1993)
Beiträge zur Algebra und Geometrie
Cube-Tilings of Rn and Nonlinear Codes.
J.C. Lagarias, P.W. Shor (1994)
Discrete & computational geometry
Curvature flows of maximal integral triangulations
Roland Bacher (1999)
Annales de l'institut Fourier
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.
M. Laczkovich (1995)
Discrete & computational geometry
Dihedral -tilings of the sphere by rhombi and triangles.
Breda, Ana M., Santos, Altino F. (2005)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
Dihedral f-tilings of the sphere by spherical triangles and equiangular well-centered quadrangles.
Breda, Ana M.d'Azevedo, Santos, Altino F. (2004)
Beiträge zur Algebra und Geometrie
Dissections of Regular Polygons into Triangles of Equal Areas.
E.A. Kasimatis (1989)
Discrete & computational geometry
Distinct equilateral triangle dissections of convex regions
Diane M. Donovan, James G. Lefevre, Thomas A. McCourt, Nicholas J. Cavenagh (2012)
Commentationes Mathematicae Universitatis Carolinae
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.
Broughton, S.Allen, Haney, Dawn M., McKeough, Lori T., Smith Mayfield, Brandy (2000)
The New York Journal of Mathematics [electronic only]
Domino tilings and products of Fibonacci and Pell numbers.
Sellers, James A. (2002)
Journal of Integer Sequences [electronic only]
El diámetro de ciertos digrafos circulantes de triple paso.
Paz Morillo Bosch, Miguel Angel Fiol Mora (1986)
Stochastica
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.
Helfgott, Harald A., Gessel, Ira M. (1999)
The Electronic Journal of Combinatorics [electronic only]
Factoring an odd abelian group by lacunary cyclic subsets
Sándor Szabó (2010)
Discussiones Mathematicae - General Algebra and Applications
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.
Corrádi, Keresztély, Szabó, Sándor (2009)
Integers
Filling a box with translates of two bricks.
Kolountzakis, Mihail N. (2004)
The Electronic Journal of Combinatorics [electronic only]