• Corpus ID: 15059562

Invariant Submodules and Semigroups of Self-Similarities for Fibonacci Modules

@article{Baake1998InvariantSA,
  title={Invariant Submodules and Semigroups of Self-Similarities for Fibonacci Modules},
  author={Michael Baake and Robert V. Moody},
  journal={arXiv: Mathematical Physics},
  year={1998}
}
  • M. BaakeR. Moody
  • Published 4 September 1998
  • Mathematics
  • arXiv: Mathematical Physics
The problem of invariance and self-similarity in Z-modules is investigated. For a selection of examples relevant to quasicrystals, especially Fibonacci modules, we determine the semigroup of self-similarities and encapsulate the number of similarity submodules in terms of Dirichlet series generating functions. 

Similarity submodules and semigroups

The similarity submodules for various lattices and modules of interest in the crystal and quasicrystal theory are determined and the corresponding semigroups, along with their zeta functions, are

Similarity Submodules and Root Systems in Four Dimensions

Abstract Lattices and $\mathbb{Z}$ -modules in Euclidean space possess an infinitude of subsets that are images of the original set under similarity transformation. We classify such self-similar

Similar sublattices of the root lattice A4

References

SHOWING 1-10 OF 19 REFERENCES

Similarity submodules and semigroups

The similarity submodules for various lattices and modules of interest in the crystal and quasicrystal theory are determined and the corresponding semigroups, along with their zeta functions, are

Combinatorial aspects of colour symmetries

The problem of colour symmetries of crystals and quasicrystals is investigated from its combinatorial point of view. For various lattices and modules in two and three dimensions, the number of

Colourings of quasicrystals

We introduce a notion of colouring the points of a quasicrystal analogous to the idea of colouring or grading of the points of a lattice. Our results apply to quasicrystals that can be coordinatized

The Mathematics of Long-Range Aperiodic Order

Preface. Knotted Tilings C.C. Adams. Solution of the Coincidence Problem in Dimensions d smaller than or equal to 4 M. Baake. Self-Similar Tilings and Patterns Described by Mappings C. Bandt. Delone

Planar coincidences for N‐fold symmetry

The coincidence problem for planar patterns with N‐fold symmetry is considered. For the N‐fold symmetric module with N<46, all isometries of the plane are classified that result in coincidences of

Quasicrystals and icosians

A family of quasicrystals of dimensions 1, 2, 3, 4 governed by the root lattice E8 is constructed. The use of the icosian ring, found in the quaternions with coefficients in Q( square root 5), allows

Theory of color symmetry for periodic and quasiperiodic crystals

The author presents a theory of color symmetry applicable to the description and classification of periodic as well as quasiperiodic colored crystals. This theory is an extension to multicomponent

Introduction to analytic number theory

This is the first volume of a two-volume textbook which evolved from a course (Mathematics 160) offered at the California Institute of Technology during the last 25 years. It provides an introduction

Introduction to Cyclotomic Fields

1 Fermat's Last Theorem.- 2 Basic Results.- 3 Dirichlet Characters.- 4 Dirichlet L-series and Class Number Formulas.- 5 p-adic L-functions and Bernoulli Numbers.- 5.1. p-adic functions.- 5.2. p-adic

Lattice Color Groups of Quasicrystals

Lattice color groups are introduced and used to study the partitioning of a periodically- or quasiperiodically-ordered set of points into N symmetry-related subsets. Applications range from magnetic