Fecha: Martes 14 de diciembre del 2021
Expositor: Hugo Maturana Cornejo
Título: Necessary conditions for tiling finitely generated amenable groups
We consider a set of necessary conditions which are efficient heuristics for deciding when a set of Wang tiles cannots tile a group.
Piantadosi gave necessary and sufficient conditions for the existence of a valid tiling of any free group. This condition is actually necessary for the existence of a valid tiling for an arbitrary finitely generated group.
We consider two conditions: the first, also given by Piantadosi, is a necessary and sufficient condition to decide if a set of Wang tiles gives a strongly periodic tiling of the free group; the second, given by Chazottes et al, is a necessary condition to decide if a set of Wang tiles gives a tiling of Z^2.
We show that these last two conditions are equivalent. Joining and generalising approaches from both sides, we prove that they are necessary for having a valid tiling of any finitely generated amenable group, confirming a remark of Jeandel.
Joint work with: Benjamin Hellouin de Menibus.