Invariant Submodules and Semigroups of Self-Similarities for Fibonacci Modules

Details Invariant Submodules and Semigroups of Self-Similarities for Fibonacci Modules Invariant Submodules and Semigroups of Self-Similarities for Fibonacci Modules

1998-09-04

arxiv.org/abs/math-ph/9809008v1

Aperiodic 97, eds. M. de Boissieu et al., World Scientific, Singapore (1998), pp. 21-27.

Physics

Mathematical Physics

7 pages; to appear in: Aperiodic 97, eds. M. de Boissieu, J. L. Verger-Gaugry and R. Currat, World Scientific, Singapore (1998

Scientific paper

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.

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