21 citations · 107 across the 30 of their papers we have counts for
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A characterization of finite sets that tile the integers
Andrew Granville, Izabella Laba, Yang Wang
We consider the problem of characterizing finite sets which tile the integers by translations. Coven and Meyerowitz (J. Algebra 1999) found necessary and sufficient conditions for…
On spectral Cantor measures
Izabella Laba, Yang Wang
A probability measure in R^d is called a spectral measure if it has an orthonormal basis consisting of exponentials. In this paper we study spectral Cantor measures. We establish a…
On sets of integers not containing long arithmetic progressions
Izabella Laba, Michael T. Lacey
We construct subsets of {1,...,N} of cardinality at least N exp(-C(log N)^{1/(k+1)}) which do not contain arithmetic progressions of length 2^k+1. This extends a result of Behrend…
Tiling and spectral properties of near-cubic domains
Mihail N. Kolountzakis, Izabella Laba
We prove that is a measurable domain tiles R or R^2 by translations, and if it is "close enough" to a line segment or a square respectively, then it admits a lattice tiling. We als…