52 citations · 151 across the 7 of their papers we have counts for
7 papers
Entropy and diffraction of the -free points in -dimensional lattices
Peter A. B. Pleasants, Christian Huck
We consider the th-power-free points in -dimensional lattices and explicitly calculate their entropies and diffraction spectra. This is of particular interest since these set…
Coincidence site modules in 3-space
Michael Baake, Peter Pleasants, Ulf Rehmann
The coincidence site lattice (CSL) problem and its generalization to Z-modules in Euclidean 3-space is revisited, and various results and conjectures are proved in a unified way, b…
Planar coincidences for N-fold symmetry
Peter A. B. Pleasants, Michael Baake, Johannes Roth
The coincidence problem for planar patterns with -fold symmetry is considered. For the N-fold symmetric module with , all isometries of the plane are classified that resul…
A maximum density rule for surfaces of quasicrystals
Z. Papadopolos, P. Pleasants, G. Kasner +6
A rule due to Bravais of wide validity for crystals is that their surfaces correspond to the densest planes of atoms in the bulk of the material. Comparing a theoretical model of i…
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…
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…