I. Laba

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math.CO2024

Splitting for integer tilings

Izabella Åaba, Itay Londner

We consider translational integer tilings by finite sets $A \subset Z$ . We introduce a new method based on \emph{splitting}, together with a new combinatorial interpretation…

math.CO2024

The Coven-Meyerowitz tiling conditions for 3 prime factors: the even case

Izabella Laba, Itay Londner

We consider finite sets $A \subset Z$ tiles the integers by translations. By periodicity, any such tiling is equivalent to a factorization $A \oplus B = Z_{M}$ of a fini…

math.CO2024

Keller properties for integer tiling

Benjamin Bruce, Izabella Laba

Keller's conjecture on cube tilings asserted that, in any tiling of $R^{d}$ by unit cubes, there must exist two cubes that share a $(d - 1)$ -dimensional face. This is now know…