3 papers
math.CO2024
Periodicity and decidability of translational tilings by rational polygonal sets
Jaume de Dios Pont, Jan Grebík, Rachel Greenfeld +1
The periodic tiling conjecture asserts that if a region tiles by translations then it admits at least one fully periodic tiling. This conjectur…
math.CO2022
A counterexample to the periodic tiling conjecture (announcement)
Rachel Greenfeld, Terence Tao
The periodic tiling conjecture asserts that any finite subset of a lattice which tiles that lattice by translations, in fact tiles periodically. We announce here a d…
math.CA2020
The structure of translational tilings in
Rachel Greenfeld, Terence Tao
We obtain structural results on translational tilings of periodic functions in by finite tiles. In particular, we show that any level one tiling of a periodic set in…