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Functional tilings and the Coven-Meyerowitz tiling conditions
Gergely Kiss, Itay Londner, Máté Matolcsi +1
Coven and Meyerowitz formulated two conditions which have since been conjectured to characterize all finite sets that tile the integers by translation. By periodicity, this conject…
A lonely weak tile
Gergely Kiss, Itay Londner, Máté Matolcsi +1
The notion of weak tiling was a key ingredient in the proof of Fuglede's spectral set conjecture for convex bodies \cite{conv}, due to the fact that every spectral set tiles its co…
Splitting for integer tilings
Izabella Łaba, Itay Londner
We consider translational integer tilings by finite sets . We introduce a new method based on \emph{splitting}, together with a new combinatorial interpretation…
The Coven-Meyerowitz tiling conditions for 3 prime factors: the even case
Izabella Laba, Itay Londner
We consider finite sets tiles the integers by translations. By periodicity, any such tiling is equivalent to a factorization of a fini…
The Coven-Meyerowitz tiling conditions for 3 odd prime factors
Izabella Laba, Itay Londner
It is well known that if a finite set tiles the integers by translations, then the translation set must be periodic, so that the tiling is equivalent to a fact…
Combinatorial and harmonic-analytic methods for integer tilings
Izabella Laba, Itay Londner
A finite set of integers tiles the integers by translations if can be covered by pairwise disjoint translated copies of . Restricting attention to one tiling pe…