Image sampling with quasicrystals.
Improved Bounds for the Disk-packing Constant
Improved coverings of a square with six and eight equal circles.
Improved inclusion-exclusion inequalities for simplex and orthant arrangements.
Improving dense packings of equal disks in a square.
Inequalities for lattice constrained planar convex sets.
Infinite perfekte Dreieckszerlegungen auch für gleichseitige Dreiecke.
Infinite periodic discrete minimal surfaces without self-intersections.
Inflationary tilings with a similarity structure.
Inhomogeneous extreme forms
G.F. Voronoi (1868–1908) wrote two memoirs in which he describes two reduction theories for lattices, well-suited for sphere packing and covering problems. In his first memoir a characterization of locally most economic packings is given, but a corresponding result for coverings has been missing. In this paper we bridge the two classical memoirs.By looking at the covering problem from a different perspective, we discover the missing analogue. Instead of trying to find lattices giving economical...
Integer partitions, tilings of -gons and lattices
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of -gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a -gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.
Integer Partitions, Tilings of 2D-gons and Lattices
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of 2D-gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a 2D-gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.
Integer Points on Curves and Surfaces.
Integral Self-Affine Tiles in ... Part II: Lattice Tilings.
Interpretations of the -vector.
Intrinsic Volumes and Lattice Points of Crosspolytopes.
Introduction aux quasicristaux
Introduction aux quasicristaux
Ionpackings in the space
Isohedrally compatible tilings