About some Riemann surfaces and plane tilings.
About the domino problem in the hyperbolic plane from an algorithmic point of view
This paper is a contribution to the general tiling problem for the hyperbolic plane. It is an intermediary result between the result obtained by R. Robinson [Invent. Math.44 (1978) 259–264] and the conjecture that the problem is undecidable.
Affine perimeter and limit shape.
Affine-regular hexagons of extreme areas inscribed in a centrally symmetric convex body.
Alexander duality in subdivisions of Lawrence polytopes.
Alexandrov’s theorem, weighted Delaunay triangulations, and mixed volumes
We present a constructive proof of Alexandrov’s theorem on the existence of a convex polytope with a given metric on the boundary. The polytope is obtained by deforming certain generalized convex polytopes with the given boundary. We study the space of generalized convex polytopes and discover a connection with weighted Delaunay triangulations of polyhedral surfaces. The existence of the deformation follows from the non-degeneracy of the Hessian of the total scalar curvature of generalized convex...
Algorithms for Triangulating Polyhedra Into a Small Number of Tethraedra
Ammann Bars and Quasicrystals.
An algorithm for deciding if a polyomino tiles the plane
For polyominoes coded by their boundary word, we describe a quadratic O(n2) algorithm in the boundary length n which improves the naive O(n4) algorithm. Techniques used emanate from algorithmics, discrete geometry and combinatorics on words.
An alternative proof of Petty's theorem on equilateral sets
The main goal of this paper is to provide an alternative proof of the following theorem of Petty: in a normed space of dimension at least three, every 3-element equilateral set can be extended to a 4-element equilateral set. Our approach is based on the result of Kramer and Németh about inscribing a simplex into a convex body. To prove the theorem of Petty, we shall also establish that for any three points in a normed plane, forming an equilateral triangle of side p, there exists a fourth point,...
An arrangement of pseudocircles not realizable with circles.
An axiomatic approach for the Hajós theorem.
An edge-minimization problem for regular polygons.
An Ehrhart series formula for reflexive polytopes.
An elementary chromatic reduction for gain graphs and special hyperplane arrangements.
An elementary proof of Blundon's inequality.
An exact method for the 2D guillotine strip packing problem.
An Example Concerning the Translative Kissing Number of a Convex Body.
An Invariant Property of Balls in Arrangements of Hyperplanes.
An On-Line Potato-Sack Theorem.