21 citations · 107 across the 30 of their papers we have counts for
8 papers · 1 filter
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…
Keller properties for integer tiling
Benjamin Bruce, Izabella Laba
Keller's conjecture on cube tilings asserted that, in any tiling of by unit cubes, there must exist two cubes that share a -dimensional face. This is now know…
Generalized polynomials and hyperplane functions in
Izabella Łaba, Charlotte Trainor
For prime, let be the linear span of characteristic functions of hyperplanes in . We establish new upper bounds on the dimension o…
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…
Incidence theorems for pseudoflats
Izabella Laba, Jozsef Solymosi
We prove Pach-Sharir type incidence theorems for a class of curves in R^n and surfaces in R^3, which we call pseudoflats. In particular, our results apply to a wide class of generi…