Sigrid Grepstad

collaborators

4 papers

math.MG2026

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 CieÅla and Sabok to prove that (i) if two measurable sets $A, B \subset R^{d}$ of the same measure are bounded remainder sets wit…

math.DS2026

Bounded distance equivalence of cut-and-project sets and equidecomposability

Sigrid Grepstad

We show that given a lattice $I^ \subset R^{m} \times R^{n}$ , and projections $p_{1}$ and $p_{2}$ onto $R^{m}$ and $R^{n}$ respectively, cut-and-project sets…

math.CA2025

Bounded common fundamental domains for two lattices

Sigrid Grepstad, Mihail N. Kolountzakis

We prove that for any two lattices $L, M \subseteq R^{d}$ of the same volume there exists a measurable, bounded, common fundamental domain of them. In other words, there exi…

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…