18 citations · 43 across the 10 of their papers we have counts for
10 papers
Catalan numbers as discrepancies for a family of substitutions on infinite alphabets
Dirk Frettlöh, Alexey Garber, Neil Mañibo
In this work, we consider a class of substitutions on infinite alphabets and show that they exhibit a growth behaviour which is impossible for substitutions on finite alphabets. Wh…
Fair partitions of the plane into incongruent pentagons
Dirk Frettlöh, Christian Richter
Motivated by a question of R.\ Nandakumar, we show that the Euclidean plane can be dissected into mutually incongruent convex pentagons of the same area and the same perimeter.
Incongruent equipartitions of the plane into quadrangles of equal perimeter
Dirk Frettlöh, Christian Richter
Motivated by a question of R.\ Nandakumar, we show that the Euclidean plane can be dissected into mutually incongruent convex quadrangles of the same area and the same perimeter. A…
Pisot substitution sequences, one dimensional cut-and-project sets and bounded remainder sets with fractal boundary
Dirk Frettlöh, Alexey Garber
This paper uses a connection between bounded remainder sets in and cut-and-project sets in together with the fact that each one-dimensional Pisot substi…
Substitution tilings with dense tile orientations and n-fold rotational symmetry
Dirk Frettlöh, April L. D. Say-awen, M. L. A. N. de las Peñas
It is shown that there are primitive substitution tilings with dense tile orientations invariant under n-fold rotation for n=2,3,4,5,6,8. The proof for dense tile orientations uses…
Dynamical properties of almost repetitive Delone sets
Dirk Frettlöh, Christoph Richard
We consider the collection of uniformly discrete point sets in Euclidean space equipped with the vague topology. For a point set in this collection, we characterise minimality of a…
Parallelogram tilings, Worms and Finite Orientations
Dirk Frettlöh, Edmund Harriss
This paper studies properties of tilings of the plane by parallelograms. In particular it is established that in parallelogram tilings using a finite number of shapes all tiles occ…
Selfdual Substitutions in Dimension One
Valérie Berthé, Dirk Frettlöh, Victor Sirvent
There are several notions of the 'dual' of a word/tile substitution. We show that the most common ones are equivalent for substitutions in dimension one, where we restrict ourselve…
Perfect colourings of cyclotomic integers
E. P. Bugarin, M. L. A. N. de las Peñas, D. Frettlöh
Perfect colourings of the rings of cyclotomic integers with class number one are studied. It is shown that all colourings induced by ideals (q) are chirally perfect, and vice versa…
SCD Patterns Have Singular Diffraction
Michael Baake, Dirk Frettlöh
Among the many families of nonperiodic tilings known so far, SCD tilings are still a bit mysterious. Here, we determine the diffraction spectra of point sets derived from SCD tilin…