Rachel Greenfeld

activity

20162026

most citedFuglede's spectral set conjecture for convex polytopes

50 citations · 96 across the 16 of their papers we have counts for

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6 papers · 1 filter

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 $Σ \subset R^{d}$ tiles $R^{d}$ by translations then it admits at least one fully periodic tiling. This conjectur…

math.CO2023★ 3 cited

Undecidability of translational monotilings

Rachel Greenfeld, Terence Tao

In the 60's, Berger famously showed that translational tilings of $Z^{2}$ with multiple tiles are algorithmically undecidable. Recently, Bhattacharya proved the decidability…

math.CO2022★ 18 cited

A counterexample to the periodic tiling conjecture

Rachel Greenfeld, Terence Tao

The periodic tiling conjecture asserts that any finite subset of a lattice $Z^{d}$ which tiles that lattice by translations, in fact tiles periodically. In this work we disp…

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 $Z^{d}$ which tiles that lattice by translations, in fact tiles periodically. We announce here a d…

math.CO2021★ 1 cited

Additive energies on discrete cubes

Jaume de Dios Pont, Rachel Greenfeld, Paata Ivanisvili +1

We prove that for $d \geq 0$ and $k \geq 2$ , for any subset $A$ of a discrete cube ${0, 1}^{d}$ , the $k -$ higher energy of $A$ (the number of $2 k -$ tuples $(a_{1}, a_{2}, \dots, a_{2 k})$ in $A…

math.CO2021

Undecidable translational tilings with only two tiles, or one nonabelian tile

Rachel Greenfeld, Terence Tao

We construct an example of a group $G = Z^{2} \times G_{0}$ for a finite abelian group $G_{0}$ , a subset $E$ of $G_{0}$ , and two finite subsets $F_{1}, F_{2}$ of $G$ , such that it is u…