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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…
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…