On pattern entropy of weak model sets
Combinatorics
2015-09-10 v4 Mathematical Physics
Dynamical Systems
math.MP
Abstract
We study point sets arising from cut-and-project constructions. An important class is weak model sets, which include squarefree numbers and visible lattice points. For such model sets, we give a non-trivial upper bound on their pattern entropy in terms of the volume of the window boundary in internal space. This proves a conjecture by R.V. Moody.
Cite
@article{arxiv.1412.6307,
title = {On pattern entropy of weak model sets},
author = {Christian Huck and Christoph Richard},
journal= {arXiv preprint arXiv:1412.6307},
year = {2015}
}
Comments
14 pages; v3: changes in some proofs, v4: minor changes in some proofs