Showing 2025Show all
3 papers · 1 filter
math.MG2025
Bounded remainder sets, bounded distance equivalent cut-and-project sets, and equidecomposability
Mark Mordechai Etkind, Sigrid Grepstad, Mihail N. Kolountzakis +1
We use the measurable Hall's theorem due to Cieśla and Sabok to prove that (i) if two measurable sets of the same measure are bounded remainder sets with…
math.CA2025
Bounded lattice tiles that pack with another lattice
Sigrid Grepstad, Mihail N. Kolountzakis, Emmanuil Spyridakis
Suppose L and M are full-rank lattices in Euclidean space, such that vol(L) < vol(M). Answering a question of Han and Wang from 2001, we show how to construct a bounded measurable…
math.CA2025
Bounded common fundamental domains for two lattices
Sigrid Grepstad, Mihail N. Kolountzakis
We prove that for any two lattices of the same volume there exists a measurable, bounded, common fundamental domain of them. In other words, there exi…