Add to ORKGWe study the problem of finding a function $f$ with ``small support'' that simultaneously tiles with finitely many lattices $\Lambda_1, \ldots, \Lambda_N$ in $d$-dimensional Euclidean spaces. We prove several results, both upper bounds (constructions) and lower bounds on how large this support can and must be. We also study the problem in the setting of finite abelian groups, which turns out to be the most concrete setting. Several open questions are posed.Comment: 16 page
International audienceWe construct a class of polycubes that tile the space by translation in a latt...
The lattice size of a lattice polytope is a geometric invariant which was formally introduced in the...
For finite polyomino regions, tileability by a pair of rectangles is NP-complete for all but trivial...
We discuss problems of simultaneous tiling. This means that we have an object (set, function) which ...
The periodic tiling conjecture asserts that any finite subset of a lattice $\mathbb{Z^d}$ which tile...
Recently it was shown that there is no measurable Steinhaus set in R a set which no matter how tr...
The periodic tiling conjecture asserts that any finite subset of a lattice $\mathbb{Z}^d$ which tile...
My main research interest is combinatorics and discrete geometry. I study tilings in this context, w...
Let $\Omega\subset \mathbb{R}^d$ be a set of finite measure. The periodic tiling conjecture suggests...
Let $\Omega\subset \mathbb{R}^d$ be a set of finite measure. The periodic tiling conjecture suggests...
The structure of translational tilings in $\mathbb{Z}^d$, Discrete Analysis 2021:16, 28 pp. A signi...
We consider measurable functions $f$ on $\mathbb{R}$ that tile simultaneously by two arithmetic prog...
A function f 2 L 1 (R) tiles the line with a constant weight w using the discrete tile set A if P...
International audienceWe construct a class of polycubes that tile the space by translation in a latt...
International audienceWe construct a class of polycubes that tile the space by translation in a latt...
International audienceWe construct a class of polycubes that tile the space by translation in a latt...
The lattice size of a lattice polytope is a geometric invariant which was formally introduced in the...
For finite polyomino regions, tileability by a pair of rectangles is NP-complete for all but trivial...
We discuss problems of simultaneous tiling. This means that we have an object (set, function) which ...
The periodic tiling conjecture asserts that any finite subset of a lattice $\mathbb{Z^d}$ which tile...
Recently it was shown that there is no measurable Steinhaus set in R a set which no matter how tr...
The periodic tiling conjecture asserts that any finite subset of a lattice $\mathbb{Z}^d$ which tile...
My main research interest is combinatorics and discrete geometry. I study tilings in this context, w...
Let $\Omega\subset \mathbb{R}^d$ be a set of finite measure. The periodic tiling conjecture suggests...
Let $\Omega\subset \mathbb{R}^d$ be a set of finite measure. The periodic tiling conjecture suggests...
The structure of translational tilings in $\mathbb{Z}^d$, Discrete Analysis 2021:16, 28 pp. A signi...
We consider measurable functions $f$ on $\mathbb{R}$ that tile simultaneously by two arithmetic prog...
A function f 2 L 1 (R) tiles the line with a constant weight w using the discrete tile set A if P...
International audienceWe construct a class of polycubes that tile the space by translation in a latt...
International audienceWe construct a class of polycubes that tile the space by translation in a latt...
International audienceWe construct a class of polycubes that tile the space by translation in a latt...
The lattice size of a lattice polytope is a geometric invariant which was formally introduced in the...
For finite polyomino regions, tileability by a pair of rectangles is NP-complete for all but trivial...