3 papers
math.MG2001
Local Complexity of Delone Sets and Crystallinity
J. C. Lagarias, P. A. B. Pleasants
This paper characterizes when a Delone set X is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the hetereogeneity of their distr…
math.DS1999
Repetitive Delone Sets and Quasicrystals
Jeffery C. Lagarias, Peter A. B. Pleasants
This paper considers the problem of characterizing the simplest discrete point sets that are aperiodic, using invariants based on topological dynamics. A Delone set whose patch-cou…
math.MG1999
Diffraction from visible lattice points and k-th power free integers
Michael Baake, Robert V. Moody, Peter A. B. Pleasants
We prove that the set of visible points of any lattice of dimension at least 2 has pure point diffraction spectrum, and we determine the diffraction spectrum explicitly. This settl…